Displaying three-dimensional objects

ABSTRACT

Methods, apparatus, devices, and systems for displaying three-dimensional objects by individually diffracting different colors of light are provided. In one aspect, an optical device includes: a first optically diffractive component including a first diffractive structure configured to diffract a first color of light having a first incident angle at a first diffracted angle, a second optically diffractive component including a second diffractive structure configured to diffract a second color of light having a second incident angle at a second diffracted angle, a first reflective layer configured to totally reflect the first color of light having the first incident angle and transmit the second color of light, and a second reflective layer configured to totally reflect the second color of light having the second incident angle. The first reflective layer is between the first and second diffractive structures, and the second diffractive structure is between the first and second reflective layers.

INCORPORATION BY REFERENCE

The present application is a continuation of, and claims benefit under35 USC § 120 to, international applications PCT/US2021/050271 entitled“DISPLAYING THREE-DIMENSIONAL OBJECTS” and filed on Sep. 14, 2021, andPCT/US2021/050275 entitled “RECONSTRUCTING OBJECTS WITH DISPLAY ZEROORDER LIGHT SUPPRESSION” and filed on Sep. 14, 2021, which claimpriority under 35 U.S.C. § 119 to U.S. Ser. No. 63/079,707 entitled“DISPLAYING THREE-DIMENSIONAL OBJECTS” and filed on Sep. 17, 2020, andto U.S. Ser. No. 63/149,964 entitled “RECONSTRUCTING OBJECTS WITHDISPLAY ZERO ORDER LIGHT SUPPRESSION” and filed on Feb. 16, 2021. Theentire contents of each of the applications are incorporated byreference in its entirety herein.

TECHNICAL FIELD

This disclosure relates to three-dimensional (3D) displays, and moreparticularly to 3D displays with object reconstruction.

BACKGROUND

Advances in traditional two-dimensional (2D) projection and 3D renderinghave led to new approaches for 3D displays, including numerous hybridtechniques that mix head and eye tracking with conventional displaydevices for virtual reality (VR), augmented reality (AR), and mixedreality (MR). These techniques attempt to replicate an experience ofholographic imagery, combined with tracking and measurement-basedcalculations, to simulate stereo or in-eye light field that can berepresented by an actual hologram.

SUMMARY

The present disclosure describes methods, apparatus, devices, andsystems for reconstructing objects (e.g., 2D or 3D), particularly withdisplay zero order light suppression. The present disclosure providestechniques that can efficiently suppress display zero order light (e.g.,reflected, diffracted, or transmitted) from a display in a reconstructedholographic scene (or holographic content) to improve an effect of theholographic scene and accordingly a performance of a display system. Asan example, when light illuminates a display for holographicreconstruction, a portion of the light is incident on and diffracted bydisplay elements that are modulated with a hologram to form a desiredholographic scene. The other portion of the light is incident on andreflected at gaps between the display elements on the display. Thereflected other portion of the light can be considered as at least apart (e.g., a main order) of display zero order light that may beundesirably presented in the holographic scene. The display zero orderlight can also include any other unwanted light from the display, e.g.,diffracted light at the gaps, reflected light from the display elements,or reflected light from a display cover on the display. Embodiments ofthe disclosure can suppress such display zero order light.

In some implementations, a hologram is configured such that a firstportion of light illuminated on display elements of the display isdiffracted by the display elements modulated by the hologram to have atleast one characteristic different from that of display zero order lightincluding reflected light from the display. The display zero order lightcan include a second portion of the light illuminated on gaps betweenthe display elements and reflected at the gaps without modulation of thehologram. The techniques can make use of the difference between thediffracted first portion of the light and the display zero order light(e.g., the reflected second portion of the light) to cause the displayzero order light to be suppressed in the holographic scene formed by thediffracted first portion of the light. The techniques can be appliedindividually or in a combination thereof. The techniques can be appliedto any other display systems that suppress or eliminate undesired lightfrom desired light.

In some examples, the display is configured to suppress higher orders ofthe display zero order light, e.g., by including irregular ornon-uniform display elements that have different sizes. The displayelements can have no periodicity, and can form a Voronoi pattern. Insome examples, in the holographic scene, the display zero order lightcan have a much smaller power density than the diffracted first portionof the light. That is, the display zero order light is suppressed byincreasing a signal to noise ratio of the holographic scene, e.g., bydiverging the display zero order light without divergence of thediffracted first portion of the light, or by adjusting respective phasesof the display elements within a predetermined phase range such as [0,2π], or both. In some examples, the display zero order light issuppressed by directing the display zero order light away from thediffracted first portion of the light, e.g., by illuminating the lighton the display at an incident angle and preconfiguring the hologram suchthat the diffracted first portion of the light still propagates around anormal axis and the display zero order light propagates at a reflectedangle. The display zero order light can be redirected outside of theholographic scene formed by the diffracted first portion of the light,e.g., by adding an additional optically diffractive grating structure tofurther direct the display zero order light away from the holographicscene. The display zero order light can be reflected back away from theholographic scene. The display zero order light can be also absorbedbefore the holographic scene.

In the present disclosure, the terms “zero order” and “zero-order” areused interchangeably, and the terms “first order” and “first-order” areused interchangeably.

In the present disclosure, the terms “zero order” and “zero-order” areused interchangeably, and the terms “first order” and “first-order” areused interchangeably.

One aspect of the present disclosure features a method including:illuminating a display with light, a first portion of the lightilluminating display elements of the display; and modulating the displayelements of the display with a hologram corresponding to holographicdata to i) diffract the first portion of the light to form a holographicscene corresponding to the holographic data, and ii) suppress displayzero order light in the holographic scene, the display zero order lightincluding reflected light from the display.

In some examples, illuminating the display with the light includes asecond portion of the light illuminates gaps between adjacent displayelements. The display zero order light can include at least one of: thesecond portion of the light reflected at the gaps of the display, thesecond portion of the light diffracted at the gaps of the display,reflected light from the display elements, or reflected right from adisplay cover covering the display.

The reflected light from the display forms a main order of the displayzero order light, and the display can be configured to suppress one ormore higher orders of the display zero order light, and where thedisplay elements are irregular or non-uniform. In some examples, thedisplay elements form a Voronoi pattern.

In some implementations, the method further includes: configuring thehologram such that the diffracted first portion of the light has atleast one characteristic different from that of the display zero orderlight. The at least one characteristic can include at least one of: apower density; a beam divergence; a propagating direction away from thedisplay; or a polarization state.

In some implementations, the display zero order light is suppressed inthe holographic scene with a light suppression efficiency. The lightsuppression efficiency is defined as a result of one minus a ratiobetween an amount of the display zero light in the holographic scenewith the suppression and an amount of the display zero light in theholographic scene without the suppression. In some cases, the lightsuppression efficiency is more than a predetermined percentage that isone of 50%, 60%, 70%, 80%, 90%, or 99%. In some cases, the lightsuppression efficiency is 100%.

In some implementations, the method further includes: for each of aplurality of primitives corresponding to an object, determining anelectromagnetic (EM) field contribution to each of the display elementsof the display by computing, in a global three-dimensional (3D)coordinate system, EM field propagation from the primitive to thedisplay element; and for each of the display elements, generating a sumof the EM field contributions from the plurality of primitives to thedisplay element. The holographic data can include the sums of the EMfield contributions for the display elements of the display from theplurality of primitives of the object. The holographic scene can includea reconstructed object corresponding to the object.

In some implementations, the holographic data includes respective phasesfor the display elements of the display, and the method further includesconfiguring the hologram by adjusting the respective phases for thedisplay elements to have a predetermined phase range. The predeterminedphase range can be [0, 2π].

In some implementations, adjusting the respective phases for the displayelements includes: adjusting the respective phases according to

Ø_(a) =AØ _(i) +B,

where Ø_(i) represents an initial phase value of a respective phase,Ø_(a) represents an adjusted phase value of the respective phase, and Aand B are constants.

In some implementations, adjusting the respective phases includes:adjusting the constants A and B such that a light suppression efficiencyfor the holographic scene is maximized. The light suppression efficiencycan be larger than 50%, 60%, 70%, 80%, 90%, or 99%. In some cases,adjusting the constants A and B includes adjusting the constants A and Bby a machine vision algorithm or a machine learning algorithm.

In some implementations, the method further includes: diverging thediffracted first portion of the light to form the holographic scene; anddiverging the display zero order light in or adjacent to the holographicscene. In some examples, diverging the diffracted first portion of thelight includes guiding the diffracted first portion of the light throughan optically diverging component arranged downstream the display, anddiverging the display zero order light includes guiding the display zeroorder light through the optically diverging component.

In some examples, the light illuminating the display is a collimatedlight. The display zero order light is collimated before arriving at theoptically diverging component, and the method can further includeconfiguring the hologram such that the diffracted first portion of thelight is converging before arriving at the optically divergingcomponent.

In some implementations, the holographic data includes a respectivephase for each of the display elements. The method can further includeconfiguring the hologram by adding a corresponding phase to therespective phase for each of the display elements, and the correspondingphases for the display elements can be compensated by the opticallydiverging component such that the holographic scene corresponds to therespective phases for the display elements. The corresponding phase foreach of the display elements can be expressed as:

Ø=π/2f(ax ²+by²),

where Ø represents the corresponding phase for the display element, λrepresents a wavelength of the light, f represents a focal length of theoptically diverging component, x and y represent coordinates of thedisplay element in a coordinate system, and a and b represent constants.

In some implementations, the holographic scene corresponds to areconstruction cone with a viewing angle. The method can further includeconfiguring the hologram by moving a configuration cone with respect tothe display with respect to a global 3D coordinate system along adirection perpendicular to the display with a distance corresponding toa focal length of the optically diverging component, the configurationcone corresponding to the reconstruction cone and having an apex angleidentical to the viewing angle, and generating the holographic databased on the moved configuration cone in the global 3D coordinatesystem. The plurality of primitives of the object can be in the movedconfiguration cone.

In some implementations, the optically diverging component is adefocusing element including at least one of a concave lens or aholographic optical element (HOE) configured to diffract the displayzero order light outside of the holographic scene.

In some implementations, the optically diverging component is a focusingelement including at least one of

a convex lens or a holographic optical element (HOE) configured todiffract the display zero order light outside of the holographic scene.

In some implementations, the method further includes: displaying theholographic scene on a two-dimensional (2D) screen spaced away from thedisplay along a direction perpendicular to the display. The method canfurther include: moving the 2D screen to obtain different slices of theholographic scene on the 2D screen.

In some implementations, the method further includes: guiding the lightto illuminate the display. In some examples, guiding the light toilluminate the display includes: guiding the light by a beam splitter,and the diffracted first portion of the light and the display zero orderlight transmit through the beam splitter.

In some implementations, illuminating the display with the lightincludes: illuminating the display with the light at normal incidence.

In some implementations, the diffracted first portion of the light formsa reconstruction cone with a viewing angle, and illuminating the displaywith the light includes illuminating the display with the light at anincident angle that is larger than a half of the viewing angle. In someexamples, the method further includes: configuring the hologram suchthat the diffracted first portion of the light forms the reconstructioncone that is same as a reconstruction cone to be formed by thediffracted first portion of the light if the light is normally incidenton the display.

In some examples, the holographic data includes a respective phase foreach of the display elements. The method can further include configuringthe hologram by adding a corresponding phase to the respective phase foreach of the display elements, and the corresponding phases for thedisplay elements can be compensated by the incident angle such that theholographic scene corresponds to the respective phases for the displayelements.

In some examples, the corresponding phase for each of the displayelements can be expressed as:

Ø=2π/λ(x cos θ+y cos θ),

where Ø represents the corresponding phase for the display element, λrepresents a wavelength of the light, x and y represent coordinates ofthe display element in a global 3D coordinate system, and θ representsan angle corresponding to the incident angle.

In some examples, configuring the hologram includes: moving aconfiguration cone with respect to the display with respect to a global3D coordinate system, the configuration cone corresponding to thereconstruction cone and having an apex angle corresponding to theviewing angle of the reconstruction cone, and generating the holographicdata based on the moved configuration cone in the global 3D coordinatesystem.

In some examples, moving the configuration cone with respect to thedisplay in the global 3D coordinate system includes: rotating theconfiguration cone by a rotation angle with respect to a surface of thedisplay with respect to the global 3D coordinate system, the rotationangle corresponding to the incident angle.

In some implementations, the method further includes: blocking thedisplay zero order light from appearing in the holographic scene. Alight suppression efficiency for the holographic scene can be 100%. Insome examples, blocking the display zero order light includes: guidingthe display zero order light towards an optically blocking componentarranged downstream the display. The method can further include: guidingthe diffracted first portion of the light to transmit through theoptically blocking component with a transmission efficiency to form theholographic scene. The transmission efficiency can be no less than apredetermined ratio. The predetermined ratio can be 50%, 60%, 70%, 80%,90%, or 99%.

In some implementations, the optically blocking component is configuredto transmit a first light beam having an angle smaller than apredetermined angle and block a second light beam having an angle largerthan the predetermined angle, and the predetermined angle is smallerthan the incident angle and larger than the half of the viewing angle.The optically blocking component can include a plurality ofmicrostructures or nanostructures, a metamaterial layer, or an opticallyanisotropic film.

In some implementations, the method further includes: guiding the lightto illuminate the display by guiding the light through an opticallydiffractive component on a substrate configured to diffract the lightout with the incident angle. Guiding the light to illuminate the displaycan include at least one of: guiding the light through a waveguidecoupler to the optically diffractive component, guiding the lightthrough a coupling prism to the optically diffractive component, orguiding the light through a wedged surface of the substrate to theoptically diffractive component.

In some implementations, the optically diffractive component is formedon a first surface of the substrate facing to the display, and theoptically blocking component is formed on a second surface of thesubstrate that is opposite to the first surface.

In some implementations, the method further includes: redirecting thedisplay zero order light away from the holographic scene. A lightsuppression efficiency for the holographic scene can be 100%.

In some implementations, redirecting the display zero order light awayfrom the holographic scene includes: diffracting the display zero orderlight away from the holographic scene by an optically redirectingcomponent arranged downstream the display. The optically redirectingcomponent can be configured to transmit the diffracted first portion ofthe light to form the holographic scene.

In some implementations, the optically redirecting component isconfigured such that the display zero order light is diffracted outsideof the holographic scene in a three-dimensional (3D) space along atleast one of an upward direction, a downward direction, a leftwarddirection, a rightward direction, or a combination thereof.

In some implementations, the optically redirecting component isconfigured to diffract a first light beam having an angle identical to apredetermined angle with a substantially larger diffraction efficiencythan a second light beam having an angle different from thepredetermined angle, and the predetermined angle is substantiallyidentical to the incident angle. The optically redirecting component caninclude a Bragg grating.

In some implementations, the optically diffractive component is formedon a first surface of the substrate facing to the display, and theoptically redirecting component is formed on a second surface of thesubstrate that is opposite to the first surface.

In some cases, the incident angle of the light is negative, and adiffraction angle of the display zero order light diffracted by theoptically redirecting component is negative. In some cases, the incidentangle of the light is positive, and a diffraction angle of the displayzero order light diffracted by the optically redirecting component ispositive. In some cases, the incident angle of the light is negative,and a diffraction angle of the display zero order light diffracted bythe optically redirecting component is positive. In some cases, theincident angle of the light is positive, and a diffraction angle of thedisplay zero order light diffracted by the optically redirectingcomponent is negative.

In some implementations, the optically redirecting component is coveredby a second substrate. The method can further include: absorbing, by anoptical absorber formed on at least one of a side surface of the secondsubstrate or a side surface of the substrate, the display zero orderlight redirected by the optically redirecting component and reflected byan interface between the second substrate and a surrounding medium.

In some implementations, the second substrate includes ananti-reflective coating on a surface of the second substrate opposite tothe optically redirecting component, and the anti-reflective coating isconfigured to transmit the display zero order light.

In some implementations, the display zero order light is p polarizedbefore arriving at the second substrate, and the optically redirectingcomponent is configured to diffract the display zero order light to beincident at a Brewster's angle on an interface between the secondsubstrate and a surrounding medium, such that the display zero orderlight totally transmits through the second substrate.

In some implementations, the method further includes: converting apolarization state of the display zero order light from s polarizationto p polarization before display zero order light arrives at the secondsubstrate. In some cases, converting the polarization state of thedisplay zero order light includes: converting the polarization state ofthe display zero order light by an optically polarizing device arrangedupstream the optically redirecting component with respect to thedisplay.

In some cases, converting the polarization state of the display zeroorder light includes: converting the polarization state of the displayzero order light by an optically polarizing device arranged downstreamthe optically redirecting component with respect to the display. Theoptically polarizing device can include an optical retarder and anoptical polarizer that are sequentially arranged downstream theoptically redirecting component, and the optical retarder can be formedon a side of the second substrate opposite to the optically redirectingcomponent, the optical polarizer being covered by a third substrate. Insome examples, the optical retarder includes a broadband half-wave plateand the optical polarizer includes a linear polarizer.

In some implementations, the second substrate includes: a first side ontop of the optically redirecting component and a second side opposite tothe first side. An optically blocking component can be formed on thesecond side of the second substrate and configured to transmit thediffracted first portion of the light and to absorb the display zeroorder light diffracted by the optically redirecting component.

In some implementations, the optically blocking component includes anoptically anisotropic transmitter configured to transmit a first lightbeam with an angle smaller than a predetermined angle, and absorb asecond light beam with an angle larger than the predetermined angle. Thepredetermined angle can be larger than half of the viewing angle andsmaller than a diffraction angle at which the display zero order lightis diffracted by the optically redirecting component.

In some implementations, the optically redirecting component isconfigured to diffract the display zero order light to be incident withan angle larger than a critical angle on an interface between the secondsubstrate and a surrounding medium, such that the display zero orderlight diffracted by the optically diffractive component is totallyreflected at the interface. An optical absorber can be formed on sidesurfaces of the substrate and the second substrate and configured toabsorb the totally reflected display zero order light.

In some implementations, the light includes a plurality of differentcolors of light, and the optically diffractive component is configuredto diffract the plurality of different colors of light at the incidentangle on the display.

In some implementations, the optical redirecting component includes arespective optically redirecting subcomponent for each of the pluralitydifferent colors of light. In some examples, the respective opticallyredirecting subcomponents for the plurality of different colors of lightcan be recorded in a same recording structure. In some examples, therespective optically directing subcomponents for the plurality ofdifferent colors of light are recorded in different correspondingrecording structures.

In some implementations, the optical redirecting component is configuredto diffract the plurality of different colors of light at differentdiffraction angles towards different directions in a 3D space. Theoptical redirecting component can be configured to diffract at least oneof the plurality of different colors of light to be incident at at leastone Brewster's angle at an interface. The interface can include one of:an interface between a top substrate and a surrounding medium, or aninterface between two adjacent substrates.

In some implementations, the optical redirecting component is configuredto diffract a first color of light and a second color of light within aplane, and a third color of light orthogonal to the plane. In someimplementations, the optical redirecting component includes at least twodifferent optically redirecting subcomponents configured to diffract asame color of light of the plurality of different colors of light. Thetwo different optically redirecting subcomponents can be sequentiallyarranged in the optical redirecting component.

In some implementations, guiding the light to illuminate the displayincludes: sequentially guiding the plurality of different colors oflight to illuminate the display in a series of time periods. In someimplementations, the optical redirecting component includes a switchableoptically redirecting subcomponent configured to diffract a first colorof light at a first state during a first time period and transmit asecond color of light at a second state during a second time period. Insome implementations, the optical redirecting component includes aswitchable optically redirecting subcomponent configured to diffract afirst color of light at a first state during a first time period anddiffract a second color of light at a second state during a second timeperiod.

In some implementations, the plurality of different colors of lightincludes a first color of light and a second color of light, the firstcolor of light having a shorter wavelength than the second color oflight, and in the optically redirecting component, a first opticallyredirecting subcomponent for the first color of light is arranged closerto the display than a second optically redirecting subcomponent for thesecond color of light.

In some implementations, fringe planes of at least two opticallyredirecting subcomponents for at least two different colors of light areoriented substantially differently.

In some implementations, the optically redirecting component includes: afirst optically redirecting subcomponent configured to diffract a firstcolor of light; a second optically redirecting subcomponent configuredto diffract a second color of light; and at least one opticallypolarizing device arranged between the first and second opticallyredirecting subcomponents and configured to convert a polarization stateof the first color of light such that the first color of light transmitsthrough the second optically redirecting subcomponent. The at least oneoptically polarizing device can include optical retarder and an opticalpolarizer that are sequentially arranged downstream the first opticallyredirecting subcomponent.

In some cases, a half of the viewing angle is within a range from −10degrees to 10 degrees or a range from −5 degrees to 5 degrees. In somecases, the incident angle is −6 degrees or 6 degrees.

Another aspect of the present disclosure features a method including:illuminating a display with light, a portion of the light illuminatingdisplay elements of the display; and generating a holographic scene bydiffracting the portion of light, while suppressing display zero orderlight present in the holographic scene, where the display zero orderlight includes reflected light from the display.

In some implementations, suppressing the display zero order lightpresent in the holographic scene includes: diverging the display zeroorder light.

In some implementations, generating a holographic scene by diffractingthe portion of light includes modulating the display elements with ahologram. Suppressing the display zero order light present in theholographic scene can include adjusting a phase range of the hologram.

In some implementations, illuminating the display with the lightincludes illuminating the display with the light at an incident angle,and suppressing the display zero order light present in the holographicscene can include modulating the portion of light with a hologramconfigured such that the portion of the light is diffracted by thedisplay elements at a diffraction angle different from a reflected angleat which the reflected light is reflected. In some cases, suppressingthe display zero order light present in the holographic scene includes:blocking the display zero order light by an incident angle dependentmaterial. The incident angle dependent material can include ametamaterial or an optically anisotropic material.

In some implementations, suppressing the display zero order lightpresent in the holographic scene includes: redirecting the display zeroorder light. Redirecting the display zero order light can includediffracting the display zero order light by an optically diffractivecomponent. The light can include different colors of light, andredirecting the display zero order light can include diffracting thedifferent colors of light to different directions in a three-dimensional(3D) space.

In some implementations, suppressing the display zero order lightpresent in the holographic scene includes: suppressing the display zeroorder light with a light suppression efficiency no less than apredetermined ratio. The light suppression efficiency is defined as aresult of one minus a ratio between an amount of the display zero orderlight in the holographic scene with the suppression and an amount of thedisplay zero order light without the suppression. The predeterminedratio can be 50%, 60%, 70%, 80%, 90%, or 100%.

Another feature of the present disclosure features an optical deviceincluding: an optically diffractive component and an optically blockingcomponent. The optically diffractive component is configured to diffractlight at an incident angle to illuminate a display, with a portion ofthe light illuminating display elements of the display, and theoptically blocking component is configured to block display zero orderlight in a holographic scene formed by the portion of the lightdiffracted by the display elements, the display zero order lightincluding reflected light from the display.

In some implementations, the optical device is configured to perform themethod as described above.

In some implementations, the display is configured to be modulated witha hologram corresponding to holographic data to diffract the portion ofthe light to form the holographic scene, and the optically blockingcomponent is configured to transmit the diffracted portion of the lightto form the holographic scene. The diffracted portion of the light canform a reconstruction cone with a viewing angle, and the incident anglecan be larger than a half of the viewing angle.

The optically blocking component can be configured to transmit a firstlight beam having an angle smaller than a predetermined angle and blocka second light beam having an angle larger than the predetermined angle,and the predetermined angle can be smaller than the incident angle andlarger than the half of the viewing angle.

In some implementations, the optically blocking component includes ametamaterial layer or an optically anisotropic film. In someimplementations, the optically blocking component includes a pluralityof microstructures or nanostructures.

In some implementations, the optical device further includes a substratehaving opposite sides. The optically diffractive component and theoptically blocking component can be formed on the opposite sides of thesubstrate.

Another aspect of the present disclosure features a method offabricating the optical device as described above, including: formingthe optically diffractive component on a first side of a substrate andforming the optically blocking component on a second side of thesubstrate opposite to the first side.

Another aspect of the present disclosure features an optical deviceincluding: an optically diffractive component and an opticallyredirecting component. The optically diffractive component is configuredto diffract light at an incident angle onto a display including aplurality of display elements spaced with gaps on the display. Thedisplay is configured to diffract a portion of the light illuminatingthe display elements. The optically redirecting component is configuredto transmit the portion of the light to form a holographic scene and toredirect display zero order light away from the holographic scene in athree-dimensional (3D) space, the display zero order light includingreflected light from the display.

In some examples, the optically redirecting component includes a Bragggrating.

In some implementations, the optically diffractive component is formedon a first side of a substrate facing to the display, and the opticallyredirecting component is formed on a second side of the substrate thatis opposite to the first side.

In some implementations, the optical device further includes a secondsubstrate covering the optically redirecting component. In someimplementations, the optical device further includes an optical absorberformed on at least one of a side surface of the substrate or a sidesurface of the second substrate, and the optical absorber is configuredto absorb the display zero order light redirected by the opticallyredirecting component and reflected by an interface between the secondsubstrate and a surrounding medium.

In some implementations, the optical device further includes: ananti-reflective coating formed on the second substrate and beingopposite to the optically redirecting component, the anti-reflectivecoating being configured to transmit the display zero order lightredirected by the optically redirecting component.

In some implementations, the optical device further includes: anoptically polarizing device configured to convert a polarization stateof the display zero order light from s polarization to p polarizationbefore the display zero order light arrives at the second substrate, andthe optically redirecting component is configured to diffract thedisplay zero order light to be incident at a Brewster's angle on aninterface between the second substrate and a surrounding medium, suchthat the display zero order light totally transmits through the secondsubstrate. The optical polarizing device can include an optical retarderand a linear polarizer that are sequentially arranged together.

In some implementations, the optically polarizing device is arrangedupstream the optically redirecting component with respect to thedisplay. In some implementations, the optically polarizing device isformed a side of the second substrate opposite to the opticallyredirecting component, the optically polarizing device being covered bya third substrate.

In some implementations, the optical device further includes: an opticalblocking component formed on a side of the second substrate opposite tothe optically redirecting component, the optical blocking componentbeing configured to transmit the portion of the light and to absorb thedisplay zero order light diffracted by the optically redirectingcomponent. The optically blocking component can include an opticallyanisotropic transmitter.

In some implementations, the optically redirecting component isconfigured to diffract the display zero order light to be incident withan angle larger than a critical angle on an interface between the secondsubstrate and a surrounding medium, such that the display zero orderlight diffracted by the optically diffractive component is totallyreflected at the interface.

In some implementations, the light includes a plurality of differentcolors of light. The optically diffractive component is configured todiffract the plurality of different colors of light at the incidentangle on the display, and the optical redirecting component can beconfigured to diffract display zero order light of the plurality ofdifferent colors of light reflected by the display at differentdiffraction angles towards different directions in the 3D space, thedisplay zero order light including reflected light of the plurality ofdifferent colors of light by the display.

In some implementations, the optical diffractive component includes aplurality of holographic gratings for the plurality of different colorsof light, and each of the plurality of holographic gratings isconfigured to diffract a respective color of light of the plurality ofdifferent colors of light at the incident angle on the display.

In some implementations, the optical redirecting component includes aplurality of redirecting holographic grating for the display zero orderlight of the plurality of different colors of light, and each of theplurality of redirecting holographic gratings is configured to diffractdisplay zero order light of a respective color of light of the pluralityof different colors of light at a respective diffractive angle towards arespective direction in the 3D space.

In some implementations, the optical redirecting component includes atleast two different redirecting holographic gratings configured todiffract display zero order light of a same color of light of theplurality of different colors of light.

In some implementations, the optical redirecting component includes aswitchable redirecting holographic grating configured to diffract afirst color of light at a first state during a first time period andtransmit a second color of light at a second state during a second timeperiod.

In some implementations, the optical redirecting component includes aswitchable redirecting holographic grating configured to diffract afirst color of light at a first state during a first time period anddiffract a second color of light at a second state during a second timeperiod.

In some implementations, the plurality of different colors of lightincludes a first color of light and a second color of light, the firstcolor of light having a shorter wavelength than the second color oflight, and, in the optically redirecting component, a first redirectingholographic grating for the first color of light is arranged closer tothe display than a second redirecting holographic grating for the secondcolor of light.

In some implementations, fringe planes of at least two redirectingholographic gratings for at least two different colors of light areoriented substantially differently.

In some implementations, the optically redirecting component includes: afirst redirecting holographic grating configured to diffract a firstcolor of light; a second redirecting holographic grating configured todiffract a second color of light; and at least one optical polarizingdevice arranged between the first and second redirecting holographicgratings and configured to convert a polarization state of the firstcolor of light such that the first color of light transmits through thesecond redirecting holographic grating.

In some implementations, the optical device is configured to perform themethods described above.

Another aspect of the present disclosure features a method offabricating the optical device as described above, including: formingthe optically diffractive component on a first side of a substrate; andforming the optically redirecting component on a second side of thesubstrate opposite to the first side.

Another aspect of the present disclosure features a system including: adisplay including display elements separated with gaps on the displayand an optical device configured to illuminate the display with light,with a portion of the light illuminating on the display elements. Thesystem is configured to diffract the portion of the light to form aholographic scene, while suppressing display zero order light in theholographic scene. The display zero order light can include at least oneof reflected light at the gaps, diffracted light at the gaps, reflectedlight at the display elements, or reflected light at a display covercovering the display.

In some implementations, the system further includes a controllercoupled to the display and configured to: modulate the display elementsof the display with a hologram corresponding to holographic data todiffract the portion of the light to form the holographic scenecorresponding to the holographic data. The hologram can be configuredsuch that the display zero order light is suppressed in the holographicscene.

In some implementations, the system further includes a computing deviceconfigured to generate primitives of one or more objects correspondingto the holographic scene. The system can be configured to perform themethods as described above. The optical device can include one or moreof the optical devices as described above.

In some implementations, the system further includes: an opticallydiverging device arranged downstream the optical device and configuredto diverge the display zero order light in the holographic scene. Thelight illuminating the display is a collimated light. The display zeroorder light is collimated before arriving at the optically divergingdevice, and the hologram is configured such that the diffracted portionof the light is converging before arriving at the optically divergingdevice. The optically diverging device can includes the opticallydiverging component as described above.

In some implementations, the system further includes a two-dimensional(2D) screen arranged downstream the display. In some implementations,the optical device includes a beam splitter. In some implementations,the optical device includes a waveguide having an incoupler and anoutcoupler. In some implementations, the optical device includes alightguide including a light coupler and an optically diffractivecomponent. The light coupler can include a coupling prism. The lightcoupler can also include a wedged substrate.

Another aspect of the present disclosure features a method offabricating the system of as described above.

Another aspect of the present disclosure features an optical deviceincluding: at least two beam expanders configured to expand an inputlight beam in at least two dimensions to generate an output light beamby diffracting the input light beam to adjust a beam size of the inputlight beam in the at least two dimensions. The beam size can include awidth and a height.

In some implementations, each of the at least two beam expandersincludes a respective optically diffractive device. The input light beamcan include light of a plurality of different colors, and the respectiveoptically diffractive device can be configured to diffract the light ofthe plurality of different colors at respective diffracted angles thatare substantially identical to each other.

In some examples, the respective optically diffractive device isconfigured such that, when the light of the different colors is incidenton the respective optically diffractive device, the respective opticaldiffractive device separates light of individual colors of the differentcolors while suppressing crosstalk between the different colors.

In some implementations, the respective optically diffractive deviceincludes: at least two optically diffractive components and at least onecolor-selective polarizer.

In some implementations, the respective optically diffractive deviceincludes: at least two optically diffractive components and at least onereflective layer. The at least one reflective layer can be configuredfor total internal reflection of light of at least one color.

In some implementations, the respective optically diffractive deviceincludes at least one of: one or more transmissive diffractivestructures, or one or more reflective diffractive structures.

In some implementations, the at least two beam expanders include: afirst one-dimensional beam expander configured to expand the input lightbeam in a first dimension of the at least two dimensions, to generate anintermediate light beam; and a second one-dimensional beam expanderconfigured to expand the intermediate light beam in a second dimensionof the at least two dimensions, to generate the output light beam. Theintermediate light beam has a larger beam size than the input light beamin the first dimension and a same beam size as the input light beam inthe second dimension, and the output light beam has a larger beam sizethan the intermediate light beam in the second dimension and a same beamsize as the intermediate light beam in the first dimension.

In some implementations, the optical device is configured to couple theintermediate light beam from the first one-dimensional beam expander tothe second one-dimensional beam expander using at least one of: afree-space in-air geometry, a monolithic or segmented substrate, or oneor more coupling elements.

In some implementations, the intermediate input beam includes collinearcollimated light of two or more colors, and the one or more couplingelements are configured to convert the collinear collimated light of thetwo or more colors to two or more independent collimated but notcollinear light beams with corresponding colors of the two or morecolors.

The present disclosure also describes methods, apparatus, devices, andsystems for displaying three-dimensional (3D) objects, particularly byindividually diffracting different colors of light. The presentdisclosure provides technology that can efficiently separate light ofdifferent colors or wavelengths to suppress (e.g., reduce or eliminate)crosstalk between the colors or wavelengths. The technology can alsosuppress light propagating without diffraction through an opticallydiffractive device and hitting at undesired angles onto a display,thereby suppressing undesired effects such as ghost images. Thetechnology enables to reconstruct multi-color three-dimensional lightfields or images with no or little crosstalk, sequentially orsimultaneously. The technology enables to implement an illuminationsystem to provide nearly normal polarized light beams of multipledifferent colors with relatively large incident angles. Accordingly, thetechnology enables to present light fields or images to viewers (e.g.,observers or users) in front of a display without obstruction of anilluminator, and to reduce power loss, e.g., due to reflections,diffraction, and/or scattering. The technology also enables to implementcompact optical systems for displaying three-dimensional objects.

The present disclosure provides technology that can overcome limitationspresent in known technologies. As an example, the technology disclosedherein can be implemented without the use of cumbersome wearabledevices, such as “3D glasses.” As another example, the technologydisclosed herein can optionally be implemented without being limited bythe accuracy of tracking mechanisms, the quality of the display devices,relatively long processing times and/or relatively high computationaldemands, and/or by an inability to display objects to multiple viewerssimultaneously. As a further example, the technology can be implementedwithout specialized tools and software to develop contents that extendabove and beyond the tools and software used in conventional 3D contentcreation. Various embodiments can exhibit one or more of the foregoingadvantages. For example, certain implementations of the presentdisclosure can produce real-time, full color, genuine 3D images thatappear to be real 3D objects in the world and can be viewed withoutencumbrances by multiple viewers simultaneously from different points.

One aspect of the present disclosure features a method including: foreach of a plurality of primitives corresponding to an object in athree-dimensional (3D) space, determining an electromagnetic (EM) fieldcontribution to each of a plurality of elements of a display bycomputing, in a 3D coordinate system, EM field propagation from theprimitive to the element; and for each of the plurality of elements,generating a sum of the EM field contributions from the plurality ofprimitives to the element.

The EM field contribution can include at least one of a phasecontribution or an amplitude contribution. The primitives can include atleast one of a point primitive, a line primitive, or a polygonprimitive. The primitives can include a line primitive including atleast one of a gradient color, a textured color, or any surface shadingeffect. The primitives can also include a polygon primitive including atleast one of a gradient color, a textured color, or any surface shadingeffect. The plurality of primitives can be indexed in a particularorder.

In some implementations, the method further includes obtainingrespective primitive data for each of the plurality of primitives. Therespective primitive data of each of the plurality of primitives caninclude respective color information of the primitive, and thedetermined EM field contributions for each of the elements includeinformation corresponding to the respective color information of theprimitives. The color information can include at least one of a texturedcolor or a gradient color. The respective primitive data of each of theplurality of primitives can include texture information of theprimitive. The respective primitive data of each of the plurality ofprimitives can include shading information on one or more surfaces ofthe primitive. The shading information can include a modulation on atleast one of color or brightness on the one or more surfaces of theprimitive.

In some implementations, the respective primitive data of each of theplurality of primitives includes respective coordinate information ofthe primitive in the 3D coordinate system. Respective coordinateinformation of each of the plurality of elements in the 3D coordinatesystem can be determined based on the respective coordinate informationof the plurality of primitives in the 3D coordinate system. Therespective coordinate information of each of the elements can correspondto a logical memory address for the element stored in a memory.

Determining the EM field contribution to each of the plurality ofelements for each of the plurality of primitives can includedetermining, in the 3D coordinate system, at least one distance betweenthe element and the primitive based on the respective coordinateinformation of the element and the respective coordinate information ofthe primitive. In some examples, determining the EM field contributionto each of the plurality of elements for each of the plurality ofprimitives includes: determining a first distance between a firstprimitive of the plurality of primitives and a first element of theplurality of elements based on the respective coordinate information ofthe first primitive and the respective coordinate information of thefirst element; and determining a second distance between the firstprimitive and a second element of the plurality of elements based on thefirst distance and a distance between the first element and the secondelement. The distance between the first element and the second elementcan be predetermined based on a pitch of the plurality of elements ofthe display.

In some examples, at least one of the plurality of primitives is a lineprimitive including first and second endpoints, and determining at leastone distance between the element and the primitive includes: determininga first distance between the element and the first endpoint of the lineprimitive; and determining a second distance between the element and thesecond point of the line primitive. In some examples, at least one ofthe plurality of primitives is a triangle primitive including first,second, and third endpoints, and determining at least one distancebetween the element and the primitive includes: determining a firstdistance between the element and the first endpoint of the triangleprimitive; determining a second distance between the element and thesecond point of the triangle primitive; and determining a third distancebetween the element and the third point of the triangle primitive.

In some implementations, determining the EM field contribution to eachof the plurality of elements for each of the plurality of primitivesincludes determining the EM field contribution to the element from theprimitive based on a predetermined expression for the primitive and theat least one distance. In some cases, the predetermined expression isdetermined by analytically calculating the EM field propagation from theprimitive to the element. In some cases, the predetermined expression isdetermined by solving Maxwell's equations. The Maxwell's equations canbe solved by providing a boundary condition defined at a surface of thedisplay. The boundary condition can include a Dirichlet boundarycondition or a Cauchy boundary condition. The plurality of primitivesand the plurality of elements can be in the 3D space, and a surface ofthe display can form a portion of a boundary surface of the 3D space. Insome cases, the predetermined expression includes at least one offunctions including a sine function, a cosine function, or anexponential function, and determining the EM field contribution includesidentifying a value of the at least one of the functions in a tablestored in a memory.

In some implementations, determining the EM field contribution to eachof the plurality of elements for each of the plurality of primitives andgenerating the sum of the field contributions for each of the pluralityof elements includes: determining first EM field contributions from theplurality of primitives to a first element of the plurality of elementsand summing the first EM field contributions for the first element; anddetermining second EM field contributions from the plurality ofprimitives to a second element of the plurality of elements and summingthe second EM field contributions for the second element. Determiningthe first EM field contributions from the plurality of primitives to thefirst element can include: determining an EM field contribution from afirst primitive of the plurality of primitives to the first element inparallel with determining an EM field contribution from a secondprimitive of the plurality of primitives to the first element.

In some implementations, determining the EM field contribution to eachof the plurality of elements for each of the plurality of primitivesincludes: determining first respective EM field contributions from afirst primitive of the plurality of primitives to each of the pluralityof elements; and determining second respective EM field contributionsfrom a second primitive of the plurality of primitives to each of theplurality of elements, and generating the sum of the field contributionsfor each of the plurality of elements can include: accumulating the EMfield contributions for the element by adding the second respective EMfield contribution to the first respective EM field contribution for theelement. Determining the first respective EM field contributions fromthe first primitive to each of the plurality of elements can beperformed in parallel with determining the second respective EM fieldcontributions from the second primitive to each of the plurality ofelements.

Determining the EM field contribution to each of the plurality ofelements for each of the plurality of primitives can include:determining a first EM field contribution from a first primitive of theplurality of primitives to a first element of the plurality of elementsin parallel with determining a second EM field contribution from asecond primitive of the plurality of primitives to the first element.

In some implementations, the method further includes: for each of theplurality of elements, generating a respective control signal based onthe sum of the EM field contributions from the plurality of primitivesto the element, the respective control signal being for modulating atleast one property of the element based on the sum of the EM fieldcontributions from the plurality of primitives to the element. The atleast one property of the element can include at least one of arefractive index, an amplitude index, a birefringence, or a retardance.The respective control signal can include an electrical signal, anoptical signal, a magnetic signal, or an acoustic signal. In some cases,the method further includes: multiplying a scale factor to the sum ofthe field contributions for each of the elements to obtain a scaled sumof the field contributions, and the respective control signal isgenerated based on the scaled sum of the field contributions for theelement. In some cases, the method further includes: normalizing the sumof the field contributions for each of the elements, and the respectivecontrol signal is based on the normalized sum of the field contributionsfor the element. The method can also include: transmitting therespective control signal to the element.

In some implementations, the method further includes: transmitting acontrol signal to an illuminator, the control signal indicating toactivate the illuminator such that the illuminator emits light on thedisplay. The control signal can be transmitted in response todetermining a completion of obtaining the sum of the field contributionsfor each of the plurality of elements. The modulated elements of thedisplay can cause the light to propagate in different directions to forma volumetric light field corresponding to the object in the 3D space.The volumetric light field can correspond to a solution of Maxwell'sequations with a boundary condition defined by the modulated elements ofthe display. The light can include a white light, and the display can beconfigured to diffract the white light into light with different colors.

In some implementations, the method further includes representing valuesusing fixed point number representations during calculation. Each of thevalues can be represented as integers with an implicit scale factor.

In some implementations, the method further includes performing amathematical function using fixed point number representations. Themathematical function can include at least one of sine, cosine, and arctangent. Performing the mathematical function can include receiving anexpression in a first fixed point format, and outputting a value at asecond fixed point format that has a level of accuracy different fromthat of the first fixed point format. Performing the mathematicalfunction can include looking up a table for calculation of themathematical function, wherein the table includes at least one of afully enumerated look-up table, an interpolated table, a semi-tablebased polynomial functions, and a semi-table based on full minimaxpolynomials. Performing the mathematical function can include applying aspecialized range reduction for an input. Performing the mathematicalfunction can include transforming a trigonometric calculation from arange [−π, π] into a signed 2's compliment representation in a range[−1,1].

Another aspect of the present disclosure features a method thatincludes: obtaining respective primitive data of a plurality ofprimitives corresponding to an object in a three-dimensional (3D) space;calculating first respective electromagnetic (EM) field contributionsfrom a first primitive of the plurality of primitives to each of aplurality of elements of a display; and calculating second respective EMfield contributions from a second primitive of the plurality ofprimitives to each of the plurality of elements of the display.Calculating the first respective EM field contributions from the firstprimitive is at least partially in parallel with calculating the secondrespective EM field contributions from the second primitive.

In some implementations, calculating a first EM field contribution fromthe first primitive to a first element of the plurality of elements isin parallel with calculating a second EM field contribution from asecond primitive of the plurality of primitives to the first element.The method can include calculating respective EM field contributionsfrom each of the plurality of primitives to each of the plurality ofelements. The calculation of the respective EM field contributions canbe without at least one of: expanding geometry of the object into theplurality of elements; applying visibility tests before packingwavefronts; and decision making or communication between parallelcalculations for different primitives. The calculation of the respectiveEM field contributions can be configured to cause at least one of:tuning parallel calculations for different primitives to speed, cost,size or energy optimization; reducing latency between initiating a drawand a result being ready for display; increasing accuracy using fixedpoint number representations; and optimizing computation speed byoptimizing mathematical functions.

In some implementations, the method further includes representing valuesusing fixed point number representations during calculation.Representing the values using the fixed point number representations canproceed without at least one of: denormalizing floats for gradualunderflow; handling NaN results from operations including division byzero; altering floating point rounding modes; and raising floating pointexceptions to an operating system.

In some implementations, the method further includes, for each of theplurality of elements, accumulating EM field contributions for theelement by adding the second respective EM field contribution for theelement to the first respective EM field contribution for the element.

In some implementations, the method further includes, for each of theplurality of elements, generating a respective control signal based on asum of the EM field contributions from the plurality of primitives tothe element, wherein the respective control signal is for modulating atleast one property of the element based on the sum of the EM fieldcontributions from the plurality of primitives to the element.

In some implementations, the method further includes scaling a firstprimitive adjacent to a second primitive by a predetermined factor suchthat a reconstruction of the first primitive does not overlap with areconstruction of the second primitive. The predetermined factor can bedetermined at least partially based on a resolution of the display. Themethod can further include: obtaining respective primitive data for eachof the plurality of primitives, wherein the respective primitive data ofeach of the plurality of primitives comprises respective coordinateinformation of the primitive in the 3D coordinate system; anddetermining new respective coordinate information of the first primitivebased on the respective coordinate information of the first primitiveand the predetermined factor. The method can further include determiningan EM field contribution from the first primitive to each of theplurality of elements based on the new respective coordinate informationof the first primitive. The method can further include scaling thesecond primitive by the predetermined factor. The first primitive andthe second primitive can share a common part, wherein scaling the firstprimitive comprises scaling the common part of the first primitive.Scaling the first primitive can include scaling the first primitive in apredetermined direction.

Another aspect of the present disclosure features a method thatincludes: obtaining respective primitive data of a plurality ofprimitives corresponding to an object in a three-dimensional (3D) space;scaling a first primitive adjacent to a second primitive by apredetermined factor using the respective primitive data for the firstprimitive and the second primitive; and updating the respectiveprimitive data for the first primitive based on a result of the scaling.

In some implementations, the respective primitive data of each of theplurality of primitives include respective coordinate information of theprimitive in a 3D coordinate system, and updating the respectiveprimitive data includes determining new respective coordinateinformation of the first primitive based on the respective coordinateinformation of the first primitive and the predetermined factor.

In some implementations, the predetermined factor is determined suchthat a reconstruction of the first primitive does not overlap with areconstruction of the second primitive in the 3D space.

In some implementations, the scaling is performed such that a gapbetween reconstruction of the first primitive and the second primitivein the 3D space is big enough to separate the first and secondprimitives to minimize an overlapping effect and small enough to makethe reconstruction appear seamless.

In some implementations, the predetermined factor is determined at leastpartially based on a resolution of the display or on an actual orassumed distance from the viewer to the display or to the z-depth of theprimitives within the display's 3D space.

In some implementations, the method further includes storing the updatedprimitive data for the first primitive in a buffer.

In some implementations, the scaling is performed during a renderingprocess of the object for obtaining the respective primitive data of theplurality of primitives.

In some implementations, the method further includes transmittingupdated primitive data for the plurality of primitives to a controller,wherein the controller is configured to determining respectiveelectromagnetic (EM) field contributions from each of the plurality ofprimitives to each of a plurality of elements of a display based on theupdated primitive data for the plurality of primitives.

In some implementations, the method further includes determining an EMfield contribution from the first primitive to each of a plurality ofelements of a display based on the updated primitive data of the firstprimitive.

In some implementations, the method further includes scaling the secondprimitive by the predetermined factor.

In some implementations, the first primitive and the second primitiveshare a common part, and scaling the first primitive comprises scalingthe common part of the first primitive.

In some implementations, scaling the first primitive includes scalingthe first primitive in a predetermined direction.

In some implementations, scaling the first primitive includes scaling afirst part of the first primitive by a first predetermined factor, andscaling a second part of the second primitive by a second predeterminedfactor, where the first predetermined factor is different from thesecond predetermined factor.

Another aspect of the present disclosure features a method thatincludes: obtaining a plurality of discrete cosine transform (DCT)weights of an image to be mapped on a specified surface of a particularprimitive of a plurality of primitives corresponding to an object in athree-dimensional (3D) space; and determining a respective EM fieldcontribution from the particular primitive to each of a plurality ofelements of a display by taking into consideration of an effect of theplurality of DCT weights of the image.

In some implementations, the method further includes: determining aresolution for the image to be mapped on the specified surface of theparticular primitive; and determining the plurality of DCT weights ofthe image based on the resolution.

In some implementations, the method further includes decoding the DCTweights of the image to obtain a respective DCT amplitude for each pixelof the image.

In some implementations, the method further includes storing valuesassociated with the respective DCT amplitudes of the pixels of the imagetogether with primitive data of the particular primitive. Determiningthe respective EM field contribution can include calculating therespective EM field contribution from the particular primitive to eachof the plurality of elements with the values associated with therespective DCT amplitudes of the pixels of the image.

In some implementations, the method further includes selectingparticular DCT terms to be included in the determining of the respectiveEM field contribution, each of the particular DCT terms having arespective DCT weight higher than a predetermined threshold.

Another aspect of the present disclosure features a method thatincludes: obtaining information of a given primitive and an occluder ofthe given primitive, wherein the given primitive is within a pluralityof primitives corresponding to an object in a three-dimensional (3D)space; and determining one or more particular elements of a plurality ofelements of a display that do not contribute to a reconstruction of thegiven primitive as an effect of the occluder.

In some implementations, the method further includes storing theinformation of the particular elements with the information of the givenprimitive and the occluder.

In some implementations, the determining is performed during a renderingprocess of the object for obtaining primitive data of the plurality ofprimitives.

In some implementations, the method further includes transmitting thestored information of the particular elements with the information ofthe given primitive and the occluder to a controller configured tocalculate electromagnetic (EM) contributions for the plurality ofprimitives to the plurality of elements of the display.

In some implementations, the method further includes, for each one ofthe particular elements, generating a sum of electromagnetic (EM) fieldcontributions from the plurality of primitives to the one of theparticular elements by excluding an EM field contribution from the givenprimitive to the one of the particular elements.

In some implementations, the method further includes, for each of theplurality of elements other than the particular elements, generating arespective sum of EM field contributions from the plurality ofprimitives to the element.

In some implementations, the method further includes masking an EM fieldcontribution of the particular elements to the given primitive.

In some implementations, determining the one or more particular elementsincludes: connecting the given primitive to endpoints of the occluder;extending the connection to the display to determine intersectionsbetween the connection and the display; and determining a particularrange defined by the intersections to be the particular elements that donot contribute to the reconstruction of the given primitive at theeffect of the occluder.

Another aspect of the present invention features a method that includes:obtaining information of a given primitive and an occluder of the givenprimitive, wherein the given primitive is within a plurality ofprimitives corresponding to an object in a three-dimensional (3D) space;and for each of a plurality of elements of a display, determining arespective part of the given primitive that does not make anelectromagnetic (EM) field contribution to the element as an effect ofthe occluder.

In some implementations, the method further includes storing theinformation of the respective part of the given primitive with theinformation of the given primitive and the occluder.

In some implementations, the determining is performed during a renderingprocess of the object for obtaining primitive data of the plurality ofprimitives.

In some implementations, the method further includes transmitting thestored information of the respective part of the given information withthe information of the given primitive and the occluder to a controllerconfigured to calculate electromagnetic (EM) contributions for theplurality of primitives to the plurality of elements of the display.

In some implementations, the method further includes masking an EM fieldcontribution of each of the plurality of elements to the respective partof the given primitive.

In some implementations, the method further includes, for each of theplurality of elements, generating a sum of EM field contributions fromthe plurality of primitives to the element by excluding an EM fieldcontribution from the respective part of the given primitive to theelement. Generating the sum of EM field contributions from the pluralityof primitives to the element can include subtracting the EM contributionof the respective part of the given primitive to the element from thesum of EM field contributions from the plurality of primitive to theelement without the effect of the occluder. Generating the sum of EMfield contributions from the plurality of primitives to the element caninclude summing EM field contributions from one or more other parts ofthe given primitive to the element, the respective part and the one ormore other parts forming the given primitive.

In some implementations, determining a respective part of the givenprimitive that do not make an EM field contribution to the element as aneffect of the occluder includes: connecting the element to endpoints ofthe occluder; determining intersections between the connection and thegiven primitive; and determining a particular part of the givenprimitive that is enclosed by the intersections to be the respectivepart of the given primitive that does not make the EM field contributionto the element at the effect of the occluder.

Another aspect of the present disclosure features a method that includesobtaining respective primitive data of each of a plurality of primitivescorresponding to an object in a three-dimensional (3D) space; obtainingrespective geometric specular information for each of the plurality ofprimitives; and storing the respective geometric specular informationwith respective primitive data for each of the plurality of primitives.

In some implementations, the respective geometric specular informationfor each of the plurality of primitives includes a reflectivity of asurface of the primitive upon a viewing angle.

In some implementations, the method further includes determining arespective EM field contribution from each of the plurality ofprimitives to each of a plurality of elements of a display by takinginto consideration of the respective geometric specular information forthe primitive.

Another aspect of the present disclosure features a method thatincludes: obtaining graphic data comprising respective primitive datafor a plurality of primitives corresponding to an object in athree-dimensional (3D) space; determining, for each of the plurality ofprimitives, an electromagnetic (EM) field contribution to each of aplurality of elements of a display by calculating, in a 3D coordinatesystem, an EM field propagation from the primitive to the element;generating, for each of the plurality of elements, a sum of the EM fieldcontributions from the plurality of primitives to the element;transmitting, for each of the plurality of elements, a respectivecontrol signal to the element, the control signal being for modulatingat least one property of the element based on the sum of the EM fieldcontributions to the element; and transmitting a timing control signalto an illuminator to activate the illuminator to illuminate light on thedisplay such that the light is caused by the modulated elements of thedisplay to form a volumetric light field corresponding to the object.

Another aspect of the disclosure features a method that includes: foreach of a plurality of elements of a display, altering a respectivecontrol signal with a predetermined calibration value; applying therespective altered respective control signals to the plurality ofelements of the display; measuring an output of light incident on thedisplay; and evaluating the predetermined calibration value based on themeasurement of the output of the light.

In some implementations, the predetermined calibration value is the samefor each of the plurality of elements.

In some implementations, the method further includes converting therespective control signals of the plurality of elements by adigital-to-analog converter (DAC), wherein altering the respectivecontrol signals for the plurality of elements includes altering digitalsignals of the respective control signals with the predeterminedcalibration value.

In some implementations, the predetermined value comprises a pluralityof bits.

In some implementations, the method further includes adjusting thepredetermined calibration value based on a result of the evaluation.Adjusting the predetermined calibration value can include modifying oneor more values of the plurality of bits. Adjusting the predeterminedcalibration value can include determining a combination of values of theplurality of bits based on the predetermined calibration value andanother calibration value determined from a previous evaluation.

In some implementations, the output of the light comprises a phasechange of the light or an intensity difference between the output of thelight and a background.

In some implementations, the respective control signal of the element isdetermined based on a sum of electromagnetic (EM) field contributionsfrom a plurality of primitives corresponding to an object to the elementin a 3D space.

Another aspect of the disclosure features a method that includes, foreach of a plurality of elements of a display: obtaining a respective sumof electromagnetic (EM) field contributions from a plurality ofprimitives in a three-dimensional (3D) space, the plurality ofprimitives corresponding to an object in the 3D space; applying arespective mathematical transform to the respective sum of EM fieldcontributions for the element to obtain a respective transformed sum ofEM field contributions for the element; determining a respective controlsignal based on the respective transformed sum of EM field contributionsfor the element; and modulating a property of the element based on thedetermined respective control signal for the element.

In some implementations, the method further includes: introducing lightincident on the plurality of elements of the display; measuring a firstoutput of the light; and adjusting one or more coefficients of therespective mathematical transforms of the plurality of elements based ona result of the measurement of the first output of the light. The methodcan further include: changing a depth of a holographic patterncorresponding to the object in view of the display; measuring a secondoutput of the light; and adjusting the one or more coefficients of therespective mathematical transforms based on the first and secondoutputs. The method can further include: changing the plurality ofprimitives corresponding to a first holographic pattern to a secondplurality of primitives corresponding to a second holographic pattern;measuring a second output of the light; and adjusting the one or morecoefficients of the respective mathematical transforms based on thefirst and second outputs. The first holographic pattern and the secondholographic pattern can correspond to the object. The second holographicpattern can correspond to a second object different from the objectrelated to the first holographic pattern. The first output of the lightcan be measured by an imaging sensor (e.g., a point sensor or aspatially integrating sensor or a three-dimensional sensor such as alight-field sensor). The imaging sensor can be configured to use amachine vision algorithm to determine what is being displayed andcalculate a fitness parameter. Each of the first and second holographicpatterns can include a grid of dots or other fiducial elements, whereinthe fitness parameter is at least one of: how close the dots or otherfiducial elements are together; how close the dots or other fiducialelements are to their intended positions colors and intensities; howwell centered the dots or other fiducial elements are positioned withrespect to their intended positions, and how distorted the dots or otherfiducial elements are.

In some implementations, the mathematical transform is derived from aZernike polynomial expression.

In some implementations, the mathematical transforms for the pluralityof elements vary element-by-element.

In some implementations the method further includes: reproducing asample set of known colors and intensities by illuminating the display;measuring an output light using a colorimeter device which can becalibrated to CIE standard observer curves; and defining the outputlight of the display in a color space such as a CIE color space. Themethod can further include: determining a deviation of values of thedefined output light from known standard values; and adaptingillumination into the display or the generation of output colors andintensities by the display to bring them back into alignment, e.g.,conformance with standard or desired values.

Another aspect of the disclosure features a method that includes:determining a cell gap of a liquid crystal (LC) display based on a pitchof display elements of the LC display; and calculating a minimum valueof a birefringence of an LC mixture based on the cell gap and apredetermined retardance for the LC display.

In some implementations, the method further includes improving aswitching speed of the LC display by keeping the birefringence of the LCmixture above the minimum value. Improving the switching speed caninclude at least one of: increasing dielectric anisotropy of the LCmixture; and decreasing the rotational viscosity of the LC mixture.

In some implementations, the LC display includes a liquid crystal onsilicon (LCOS or LCoS) device having a silicon backplane.

In some implementations, the LC display includes: a liquid crystallayer; a transparent conductive layer on top of the liquid crystal layeras a common electrode; and a backplane comprising a plurality of metalelectrodes on or electrically close to the bottom of the liquid crystallayer, wherein each of the plurality of metal electrodes is isolatedfrom each other, and the backplane is configured to control a voltage ofeach of the plurality of metal electrodes.

Another aspect of the disclosure features a display that includes: abackplane; and a plurality of display elements on the backplane, whereinat least two of the plurality of display elements have different sizes.

In some implementations, a larger one of the at least two displayelements comprises a buffer, and a smaller one of the at least twodisplay elements comprises no buffer. The larger display element can beconnected with a first plurality of display elements by a conductiveline, wherein the buffer is configured to buffer a voltage applied onthe conductive line such that the voltage is only applied to a secondplurality of display elements within the first plurality of displayelements, a number of the second plurality of display elements beingsmaller a number of the first plurality of display elements.

In some implementations, the buffer comprises an analog circuit in aform of a transistor or a digital circuit in a form of logic gates.

In some implementations, a size distribution of the plurality of displayelements is substantially identical to a size of a smaller one of the atleast two display elements.

In some implementations, the display is configured to be a liquidcrystal on silicon device.

Another aspect of the disclosure features a display that includes: abackplane; and a plurality of display elements on the backplane, whereinat least two of the plurality of display elements have different shapes.

In some implementations, the backplane includes a respective circuit foreach of the display elements, wherein the respective circuits for the atleast two display elements have shapes corresponding to the differentshapes of the at least two display elements.

In some implementations, a size distribution of the plurality of displayelements is substantially identical to a predetermined size.

In some implementations, the display is configured to be a liquidcrystal on silicon device.

Another aspect of the present disclosure features a method including:obtaining graphic data including respective primitive data for aplurality of primitives corresponding to an object in athree-dimensional (3D) space; determining, for each of the plurality ofprimitives, an electromagnetic (EM) field contribution to each of aplurality of elements of a display by calculating, in a 3D coordinatesystem, an EM field propagation from the primitive to the element;generating, for each of the plurality of elements, a sum of the EM fieldcontributions from the plurality of primitives to the element;transmitting, for each of the plurality of elements, a respectivecontrol signal to the element, the control signal being for modulatingat least one property of the element based on the sum of the EM fieldcontributions to the element; and transmitting a timing control signalto an illuminator to activate the illuminator to illuminate light on thedisplay such that the light is caused by the modulated elements of thedisplay to form a volumetric light field corresponding to the object.

Other embodiments of the aspects include corresponding computer systems,apparatus, and computer programs recorded on one or more computerstorage devices, each configured to perform the actions of the methods.For a system of one or more computers to be configured to performparticular operations or actions means that the system has installed onit software, firmware, hardware, or a combination of them that inoperation cause the system to perform the operations or actions. For oneor more computer programs to be configured to perform particularoperations or actions means that the one or more programs includeinstructions that, when executed by data processing apparatus, cause theapparatus to perform the operations or actions.

Another aspect of the present disclosure features a device thatincludes: one or more processors; and a non-transitory computer readablestorage medium in communication with the one or more processors andstoring instructions executable by the one or more processors and uponsuch execution cause the one or more processors to perform one or moreof the methods disclosed herein.

Another aspect of the present disclosure features a non-transitorycomputer readable storage medium storing instructions executable by oneor more processors and upon such execution cause the one or moreprocessors to perform the method according to one or more of the methodsdisclosed herein.

Another aspect of the present disclosure features a display including aplurality of elements; and a controller coupled to the display andconfigured to perform one or more of the methods disclosed herein. Thecontroller can include a plurality of computing units, each of thecomputing units being configured to perform operations on one or moreprimitives of a plurality of primitives correspond to an object in athree-dimensional (3D) space. In some implementations, the controller islocally coupled to the display, and each of the computing units iscoupled to one or more respective elements of the display and configuredto transmit a respective control signal to each of the one or morerespective elements. The computing units can be configured to operate inparallel.

The controller can include at least one of an application-specificintegrated circuit (ASIC), a field-programmable gate array (FPGA), aprogrammable gate array (PGA), a central processing unit (CPU), agraphics processing unit (GPU), or standard or custom computing cells.The display can include a spatial light modulator (SLM) including adigital micro-mirror device (DMD) or a liquid crystal on silicon (LCOSor LCoS) device. The display can be configured to be phase modulated,amplitude modulated, or phase and amplitude modulated. The controllercan be coupled to the display through a memory buffer.

In some implementations, the system includes an illuminator arrangedadjacent to the display and configured to emit light on the display. Theilluminator can be coupled to the controller and configured to be turnedon/off based on a control signal from the controller.

In some cases, the illuminator is coupled to the controller through amemory buffer configured to control amplitude or brightness of one ormore light emitting elements in the illuminator. The memory buffer forthe illuminator can have a smaller size than a memory buffer for thedisplay. A number of the light emitting elements in the illuminator canbe smaller than a number of the elements of the display. The controllercan be configured to simultaneously or sequentially activate the one ormore light emitting elements of the illuminator.

The illuminator can be a coherent light source, a semi-coherent lightsource, or an incoherent light source. In some implementations, theilluminator is configured to emit a white light, and wherein the displayis configured to diffract the white light into light with differentcolors. In some implementations, the illuminator includes two or morelight emitting elements each configured to emit light with a differentcolor. The controller can be configured to sequentially modulate thedisplay with information associated with a first color during a firsttime period and modulate the display with information associated with asecond color during a second, sequential time period, and the controllercan be configured to control the illuminator to sequentially activate afirst light emitting element to emit light with the first color duringthe first time period and a second light emitting element to emit lightwith the second color during the second time period.

In some implementations, the illuminator is arranged in front of asurface of the display and configured to emit the light on to thesurface of the display with an incident angle within a range between 0degree and 90 degrees, and the emitted light is diffracted from thedisplay. In some cases, the emitted light from the illuminator includescollimated light. In some cases, the emitted light from the illuminatorincludes divergent light. In some cases, the emitted light from theilluminator includes convergent light. In some cases, the emitted lightfrom the illuminator includes semi-collimated light.

In some implementations, the illuminator is arranged behind a rearsurface of the display and configured to emit a divergent collimated,semi-collimated, or convergent light on the rear surface of the display,and the emitted light is transmitted through the display and diffractedout of the display from a front surface of the display.

In some implementations, the illuminator includes: a light sourceconfigured to emit the light; and a waveguide coupled to the lightsource and arranged adjacent to the display, the waveguide beingconfigured to receive the emitted light from the light source and guidethe emitted light to the display. In some cases, the light from thelight source is coupled to the waveguide from a side cross-section ofthe waveguide through a light coupler. In some cases, the light sourceand the waveguide are integrated in a planar form and positioned on asurface of the display. The waveguide can be configured to guide thelight to illuminate the display uniformly.

In some cases, the waveguide is positioned on or optically close to arear surface of the display, and the light is guided to transmit intothe display and transmitted and diffracted out of the display from afront surface of the display. The controller can be positioned on a rearsurface of the waveguide. In some cases, the waveguide or lightguide ispositioned on or optically close to a front surface of the display, andwherein the light is guided to be incident on the front surface of thedisplay and reflected and diffracted back out through the front surface.

Another aspect of the present disclosure features a system including: adisplay including an array of elements; and an integrated circuitincluding an array of computing units, each of the computing units beingcoupled to one or more respective elements of the display and configuredto: compute an electromagnetic (EM) field contribution from at least oneprimitive of a plurality of primitives to each of the array of elements;and generate, for each of the one or more respective elements, arespective sum of the EM field contributions from the plurality ofprimitives to the element.

Each of the computing units can be configured to: receive, from othercomputing units of the array of computing units, computed EM fieldcontributions from other primitives of the plurality of primitives toeach of the one or more respective elements; and generate, for each ofthe one or more respective elements, the respective sum of the EM fieldcontributions by adding the received computed EM field contributionsfrom the other primitives to the element.

Each of the computing units can be configured to generate, for each ofthe one or more respective elements, a respective control signal tomodulate at least one property of the element based on the respectivesum of the EM field contributions to the element.

In some implementations, the integrated circuit includes a respectiveaccumulator configured to store an accumulation result of the computedEM field contribution from the plurality of primitives to each of theelements of the display. The integrated circuit can be configured toclear the accumulators at a beginning of a computation operation. Insome examples, the integrated circuit includes a respective memorybuffer for each of the elements, and the integrated circuit can beconfigured to accumulate the computed EM field contribution from theplurality of primitives to the element to obtain the respective sum ofthe EM field contributions as a final accumulation result in therespective accumulator and transfer the final accumulation result fromthe respective accumulator to the respective memory buffer for theelement.

In some implementations, the system further includes an illuminatorpositioned between the integrated circuit and the display and configuredto receive a control signal from the integrated circuit and illuminatelight on the display based on the control signal, and the integratedcircuit, the illuminator, and the display can be integrated as a singleunit.

Another aspect of the present disclosure features a system, including: acomputing device configured to generate data including respectiveprimitive data of a plurality of primitives corresponding to an objectin a three-dimensional (3D) space; and the system as disclosed herein.The system is configured to receive the graphic data from the computingdevice and process the graphic data for presenting the object in the 3Dspace. The computing device can include an application programminginterface (API) configured to create the primitives with the respectiveprimitive data by rendering a computer generated (CG) model of theobject.

Another aspect of the present disclosure features an optical device,including: a first optically diffractive component; a second opticallydiffractive component; and a color-selective polarizer between the firstand second optically diffractive components. When a first beam of lightincluding a first color of light in a first polarization state isincident on the first optically diffractive component, the firstoptically diffractive component diffracts the first color of light inthe first polarization state; when a second beam of light including asecond color of light in a second polarization state is incident on thecolor-selective polarizer, the color-selective polarizer converts thesecond beam of light to a third beam of light including the second colorof light in the first polarization state, the second color beingdifferent from the first color, and the second polarization state beingdifferent from the first polarization state; when the third beam oflight is incident on the second optically diffractive component, thesecond optically diffractive component diffracts the second color oflight in the first polarization state; and a diffraction efficiency withwhich the first optically diffractive component diffracts the secondcolor of light in the second polarization state is substantially smallerthan a diffraction efficiency with which the first optically diffractivecomponent diffracts the first color of light in the first polarizationstate.

Another aspect of the present disclosure features an optical deviceincluding: a first optically diffractive component; a second opticallydiffractive component; and a color-selective polarizer between the firstand second optically diffractive components. When a first color of lightis incident on the first optically diffractive component at a firstincident angle and in a first polarization state, the first opticallydiffractive component diffracts the first color of light at a firstdiffracted angle with a first diffraction efficiency; when a secondcolor of light different from the first color of light is incident onthe first optically diffractive component at a second incident angle ina second polarization state different from the first polarization state,the first optically diffractive component diffracts the second color oflight with a diffraction efficiency that is substantially less than thefirst diffraction efficiency; when the second color of light in thesecond polarization state is incident on the color-selective polarizer,the color-selective polarizer rotates a polarization state of the secondcolor of light from the second polarization state to the firstpolarization state; and when the second color of light is incident onthe second optically diffractive component at the second incident angleand in the first polarization state, the second optically diffractivecomponent diffracts the second color of light at a second diffractedangle with a second diffraction efficiency.

Another aspect of the present disclosure features an optical deviceincluding: a first optically diffractive component configured to: i)diffract a first color of light in a first polarization state incidentat a first incident angle with a first diffraction efficiency at a firstdiffracted angle; and ii) diffract a second color of light in a secondpolarization state incident at a second incident angle with adiffraction efficiency that is substantially less than the firstdiffraction efficiency; a color-selective polarizer configured to rotatea polarization state of the second color of light in the secondpolarization state incident on the color-selective polarizer from thesecond polarization state to the first polarization state; and a secondoptically diffractive component configured to diffract the second colorof light in the first polarization state incident at the second incidentangle with a second diffraction efficiency at a second diffracted angle,where the color-selective polarizer is between the first and secondoptically diffractive components.

In some implementations, the second optically diffractive component isconfigured to diffract the first color of light in the secondpolarization state at the first incident angle with a diffractionefficiency substantially smaller than the second diffraction efficiency.

In some implementations, the first optically diffractive component, thecolor-selective polarizer, and the second optically diffractivecomponent are sequentially stacked, such that the first color of lightand the second color of light are incident on the first opticallydiffractive component before the second optically diffractive component.

In some implementations, the optical device further includes: a thirdoptically diffractive component; and a second color-selective polarizerbetween the second and third optically diffractive components. Thesecond color-selective polarizer is configured to: when a third color oflight is incident in the second polarization state on the secondcolor-selective polarizer, rotate a polarization state of the thirdcolor of light from the second polarization state to the firstpolarization state. The third optically diffractive component isconfigured to: when the third color of light is incident on the thirdoptically diffractive component at a third incident angle and in thefirst polarization state, diffract the third color of light at a thirddiffracted angle with a third diffraction efficiency.

In some implementations, the color-selective polarizer is configured torotate a polarization state of the first color of light from the firstpolarization state to the second polarization state, and the secondcolor-selective polarizer is configured to rotate the polarization stateof the second color of light from the first polarization state to thesecond polarization state, without rotation of the polarization state ofthe first color of light.

In some implementations, the optical device further includes: a thirdcolor-selective polarizer configured to rotate the polarization state ofeach of the first and second colors of light from the secondpolarization state to the first polarization state, without rotation ofthe polarization state of the third color of light. The third opticallydiffractive component is between the second and third color-selectivepolarizers.

In some implementations, the third optically diffractive component isconfigured to diffract each of the first and second colors of lightincident in the second polarization state with a diffraction efficiencysubstantially smaller than the third diffraction efficiency. The firstoptically diffractive component is configured to diffract the thirdcolor of light incident in the second polarization state with adiffraction efficiency substantially smaller than the first diffractionefficiency, and the second optically diffractive component is configuredto diffract each of the first and third colors of light incident in thesecond polarization state with a diffraction efficiency substantiallysmaller than the second diffraction efficiency.

In some implementations, the second color-selective polarizer includes apair of a first sub-polarizer and a second sub-polarizer. The firstsub-polarizer is configured to rotate the polarization state of thesecond color of light from the first polarization state to the secondpolarization state, without rotation of the polarization state of eachof the first and third colors of light, and the second sub-polarizer isconfigured to rotate the polarization state of the third color of lightfrom the second polarization state to the first polarization state,without rotation of the polarization state of each of the first andsecond colors of light.

In some implementations, the optical device further includes: a fourthcolor-selective polarizer configured to rotate a polarization state ofthe first color of light from the second polarization state to the firstpolarization state, without rotation of the polarization state of eachof the second and third colors of light, where the first opticallydiffractive component is between the fourth color-selective polarizerand the color-selective polarizer.

In some implementations, each of the first, second, and third opticallydiffractive components includes a respective holographic grating formedin a recording medium. The recording medium can include a photosensitivepolymer. The recording medium can be optically transparent. Therespective holographic grating can be fixed in the recording medium.

In some implementations, each of the first, second, and third opticallydiffractive components includes a carrier film attached to a side of therecording medium. Each of the first, second, and third opticallydiffractive components can include a diffraction substrate attached toanother side of the recording medium opposite to the carrier film.

In some cases, the carrier film of the first optically diffractivecomponent is attached to a first side of the color-selective polarizer,and the diffraction substrate of the second optically diffractivecomponent is attached to a second, opposite side of the color-selectivepolarizer, and the carrier film of the second optically diffractivecomponent is attached to a first side of the second color-selectivepolarizer, and the diffraction substrate of the second opticallydiffractive component is attached to a second, opposite side of thesecond color-selective polarizer.

In some implementations, the optical device further includes asubstrate, and the first optically diffractive component is between thesubstrate and the color-selective polarizer. In some implementations,the optical devices further includes: an anti-reflective coating on asurface of the substrate. In some implementations, the optical deviceincludes: a front surface and a back surface, where the first color oflight and the second color of light are incident on the front surface,and the optical device further includes: an anti-reflective coating onthe back surface.

In some implementations, the optical device includes a plurality ofoptical components including the first optically diffractive component,the color-selective polarizer, and the second optically diffractivecomponent, where adjacent two optical components of the plurality ofcomponents are attached together through a refractive index matchingmaterial.

In some implementations, each of the first and second opticallydiffractive components includes a respective Bragg grating formed in arecording medium, and the respective Bragg grating includes a pluralityof fringe planes with a fringe tilt angle θ_(t) and a fringe spacing Λperpendicular to the fringe planes in a volume of the recording medium.

In some cases, the respective Bragg grating is configured such that,when an incident angle on the recording medium is an on-Bragg angle, arespective diffracted angle θ_(m) is satisfied with Bragg's equation asbelow:

mλ=2nΛ sin(θ_(m)−θ_(f)),

where λ represents a respective wavelength of a color of light invacuum, n represents a refractive index in the recording medium, θ_(m)represents m^(th) diffraction order Bragg angle in the recording medium,and θ_(t) represents a fringe tilt in the recording medium.

In some cases, each of the first and second incident angles issubstantially identical to the on-Bragg angle, and each of the first andsecond diffracted angles is substantially identical to first order Braggangle.

In some cases, the fringe tilt angle of the respective Bragg grating issubstantially identical to 45 degrees.

In some cases, a thickness of the recording medium is more than oneorder of magnitude larger than the fringe spacing. The thickness of therecording medium can be about 30 times larger than the fringe spacing.

In some cases, the first diffracted angle and the second diffractedangle are substantially identical to each other.

In some cases, each of the first and second diffracted angles is in arange from −10 degrees to 10 degrees. Each of the first and seconddiffracted angles can be substantially identical to 0 degrees. Each ofthe first and second diffracted angles can be in a range from −7 degreesto 7 degrees. Each of the first and second diffracted angles can besubstantially identical to 6 degrees.

In some cases, each of the first and second incident angles is in arange from 70 degrees to 90 degrees. The first incident angle and thesecond incident angle can be substantially identical to each other.

In some cases, the first polarization state is s polarization, and thesecond polarization state is p polarization.

In some implementations, the first optically diffractive component isconfigured to diffract the second color of light incident in the secondpolarization state with the diffraction efficiency that is at least oneorder of magnitude smaller than the first diffraction efficiency.

In some implementations, the color-selective polarizer is configured notto rotate a polarization state of the first color of light.

In some implementations, the optical device further includes: a secondcolor-selective polarizer configured to rotate a polarization state ofthe first color of light from the second polarization state to the firstpolarization state, without rotation of the polarization state of thesecond color of light, where the first optically diffractive componentis between the second color-selective polarizer and the color-selectivepolarizer.

In some implementations, the first optically diffractive componentincludes a first diffractive structure, and the second opticallydiffractive component including a second diffractive structure, wherethe optical device includes a first reflective layer and a secondreflective layer, where the first reflective layer is between the firstand second diffractive structures, and the second diffractive structureis between the first and second reflective layers, where the firstdiffractive structure is configured to: i) diffract first and zeroorders of the first color of light incident at the first incident angleon the first diffractive structure, the first order being diffracted atthe first diffracted angle, and the zero order being transmitted at thefirst incident angle; and ii) transmit the second color of lightincident at the second incident angle on the first diffractivestructure, where the first reflective layer is configured to: i) totallyreflect the first color of light incident on the first reflective layerat the first incident angle; and ii) transmit the second color of lightincident on the first reflective layer at the second incident angle,where the second diffractive structure is configured to diffracts firstand zero orders of the second color of light incident at the secondincident angle on the second diffractive structure, the first orderbeing diffracted at a second diffracted angle, and the zero order beingtransmitted at the second incident angle, and where the secondreflective layer is configured to totally reflect the second color oflight incident on the second reflective layer at the second incidentangle.

Another aspect of the present disclosure features an optical deviceincluding: a first optically diffractive component including a firstdiffractive structure; a second optically diffractive componentincluding a second diffractive structure; a first reflective layer; anda second reflective layer. The first reflective layer is between thefirst and second diffractive structures; the second diffractivestructure is between the first and second reflective layers; when afirst color of light is incident at a first incident angle on the firstdiffractive structure, the first diffraction structure diffracts firstand zero orders of the first color, the first order being diffracted ata first diffracted angle, and the zero order being transmitted at thefirst incident angle; when a second color of light is incident at asecond incident angle on the first diffractive structure, the firstdiffraction grating transmits the second color of light at the secondincident angle; when the first color of light is incident on the firstreflective layer at the first incident angle, the first reflective layertotally reflects the first color of light; when the second color oflight is incident on the first reflective layer at the second incidentangle, the reflective layer transmits the second color of light at thesecond incident angle; when the second color of light is incident at thesecond incident angle on the second diffractive structure, the seconddiffractive structure diffracts first and zero orders of the secondcolor of light, the first order being diffracted at a second diffractedangle, and the zero order being transmitted at the second incidentangle; and when the second color of light is incident on the secondreflective layer at the second incident angle, the second reflectivelayer totally reflects the second color of light.

Another aspect of the present disclosure features an optical deviceincluding: a first optically diffractive component including a firstdiffractive structure configured to: i) diffract first and zero ordersof a first color of light incident at a first incident angle on thefirst diffractive structure, the first order being diffracted at a firstdiffracted angle, and the zero order being transmitted at the firstincident angle; and ii) transmit a second color of light incident at asecond incident angle on the first diffractive structure; a firstreflective layer configured to: i) totally reflect the first color oflight incident on the first reflective layer at the first incidentangle; and ii) transmit the second color of light incident on the firstreflective layer at the second incident angle; a second opticallydiffractive component including a second diffractive structureconfigured to diffract first and zero orders of the second color oflight incident at the second incident angle on the second diffractivestructure, the first order being diffracted at a second diffractedangle, and the zero order being transmitted at the second incidentangle; and a second reflective layer configured to totally reflect thesecond color of light incident on the second reflective layer at thesecond incident angle, where the first reflective layer is between thefirst and second diffractive structures, and the second diffractivestructure is between the first and second reflective layers.

Another aspect of the present disclosure features an optical deviceincluding: a first optically diffractive component including a firstdiffractive structure configured to diffract a first color of lighthaving a first incident angle at a first diffracted angle; a secondoptically diffractive component including a second diffractive structureconfigured to diffract a second color of light having a second incidentangle at a second diffracted angle; a first reflective layer configuredto totally reflect the first color of light having the first incidentangle and transmit the second color of light having the second incidentangle; and a second reflective layer configured to totally reflect thesecond color of light having the second incident angle, where the firstreflective layer is between the first and second diffractive structures,and the second diffractive structure is between the first and secondreflective layers.

In some implementations, the optical device further includes: acolor-selective polarizer between the first and second diffractivestructures. The first diffractive structure can be configured to: i)diffract the first color of light in a first polarization state incidentat the first incident angle with a first diffraction efficiency; and ii)diffract the second color of light in a second polarization stateincident at the second incident angle with a diffraction efficiency thatis substantially less than the first diffraction efficiency. Thecolor-selective polarizer can be configured to rotate a polarizationstate of the second color of light in the second polarization stateincident on the color-selective polarizer from the second polarizationstate to the first polarization state. The second diffractive structurecan be configured to diffract the second color of light in the firstpolarization state incident at the second incident angle with a seconddiffraction efficiency.

In some implementations, the optical device further includes: a sidesurface and an optical absorber attached to the side surface andconfigured to absorb totally reflected light of the first and secondcolors.

In some implementations, the first reflective layer is configured tohave a refractive index smaller than that of a layer of the firstoptically diffractive component that is immediately adjacent to thefirst reflective layer, such that the first color of light having thefirst incident angle is totally reflected by an interface between thefirst reflective layer and the layer of the first optically diffractivecomponent, without totally reflecting the second color of light havingthe second incident angle.

In some implementations, the first optically diffractive componentincludes a first carrier film and a first diffraction substrate attachedto opposite sides of the first diffractive structure, the first carrierfilm being closer to the second diffractive structure than the firstdiffraction substrate, and the first carrier film can include the firstreflective layer.

In some implementations, the second optically diffractive componentincludes a second carrier film and a second diffraction substrateattached to opposite sides of the second diffractive structure, thesecond diffraction substrate being closer to the first diffractivestructure than the second carrier film, and the second reflective layeris attached to the second carrier film.

In some implementations, the optical device further includes: a thirdoptically diffractive component including a third diffractive structureconfigured to diffract first and zero orders of a third color of lightincident at a third incident angle on the third diffractive structure,the first order being diffracted at a third diffracted angle, and thezero order being transmitted at the third incident angle, and the secondreflective layer is between the second diffractive structure and thethird diffractive structure.

In some cases, each of the first and second reflective layers isconfigured to transmit the third color of light incident at the thirdincident angle.

In some implementations, the optical device further includes: a thirdreflective layer configured to totally reflect the third color of lightincident at the third incident angle on the third reflective layer,where the third diffractive structure is between the second and thirdreflective layers.

In some implementations, the second optically diffractive componentsincludes a second diffraction substrate and a second carrier filmarranged on opposite sides of the second diffractive structure, thethird optically diffractive component includes a third carrier film anda third diffraction substrate positioned on opposite sides of the thirddiffractive structure, and the second reflective layer is between thesecond and third carrier films.

In some implementations, each of the first and second diffractivestructure includes a respective holographic grating formed in arecording medium. The recording medium can include a photosensitivepolymer. The recording medium can be optically transparent.

In some implementations, each of the first and second opticallydiffractive components includes a respective Bragg grating formed in therecording medium, and the respective Bragg grating includes a pluralityof fringe planes with a fringe tilt angle θ_(t) and a fringe spacing Λperpendicular to the fringe planes in a volume of the recording medium.

In some implementations, the respective Bragg grating is configured suchthat, when an incident angle on the recording medium is an on-Braggangle, a respective diffracted angle θ_(m) is satisfied with Bragg'sequation as below:

mλ=2nΛ sin(θ_(m)−θ_(f)),

where λ represents a respective wavelength of a color of light invacuum, n represents a refractive index in the recording medium, θ_(m)represents m^(th) diffraction order Bragg angle in the recording medium,θ_(t) represents the fringe tilt in the recording medium.

Each of the first and second incident angles can be substantiallyidentical to a respective on-Bragg angle, and each of the first andsecond diffracted angles can be substantially identical to a respectivefirst order Bragg angle.

In some implementations, a thickness of the recording medium is morethan one order of magnitude larger than the fringe spacing. Thethickness of the recording medium can be about 30 times larger than thefringe spacing.

In some cases, the first diffracted angle and the second diffractedangle are substantially identical to each other. In some examples, eachof the first and second diffracted angles is in a range from −10 degreesto 10 degrees. In some examples, each of the first and second diffractedangles is substantially identical to 0 degrees. In some examples, eachof the first and second diffracted angles is substantially identical to6 degrees.

In some cases, the first incident angle is different from the secondincident angle. In some cases, the first color of light has a wavelengthsmaller (or shorter) than the second color of light, and the firstincident angle of the first color of light is larger (or longer) thanthe second incident angle of the second color of light. In some cases,each of the first and second incident angles is in a range from 70degrees to 90 degrees.

In some implementations, the optical device includes a plurality ofcomponents including the first optically diffractive component and thesecond optically diffractive component, and adjacent two components ofthe plurality of components are attached together by an intermediatelayer that includes at least one of a refractive index matchingmaterial, an OCA, a UV-cured or heat-cured optical glue, or an opticalcontacting material.

In some implementations, the second reflective layer includes theintermediate layer.

In some implementations, the optical device further includes a substratehaving a back surface attached to a front surface of the first opticallydiffractive component. The substrate can include a side surface angledto the back surface and is configured to receive a plurality ofdifferent colors of light at the side surface. An angle between the sidesurface and the back surface of the substrate can be no less than 90degrees. The substrate can be configured such that the plurality ofdifferent colors of light are incident on the side surface with anincident angle substantially identical to 0 degrees. In some cases, thesubstrate is wedged and includes a titled front surface, and an anglebetween the front surface and the side surface is less than 90 degrees.

Another aspect of the present disclosure features a system including: anilluminator configured to provide a plurality of different colors oflight and any one of the optical devices described herein. The opticaldevice is arranged adjacent to the illuminator and configured to receivethe plurality of different colors of light from the illuminator anddiffract the plurality of different colors of light.

In some implementations, the optical device is configured to diffractthe plurality of different colors of light at respective diffractedangles that are substantially identical to each other.

In some examples, each of the respective diffracted angles is in a rangeof −10 degrees to 10 degrees.

In some implementations, the system further includes: a controllercoupled to the illuminator and configured to control the illuminator toprovide each of the plurality of different colors of light.

In some implementations, the system further includes: a displayincluding a plurality of display elements, and the optical device isconfigured to diffract the plurality of colors of light to the display.

In some implementations, the controller is coupled to the display andconfigured to transmit a respective control signal to each of theplurality of display elements for modulation of at least one property ofthe display element.

In some implementations, the controller is configured to: obtain graphicdata including respective primitive data for a plurality of primitivescorresponding to an object in a three-dimensional space; determine, foreach of the plurality of primitives, an electromagnetic (EM) fieldcontribution to each of the plurality of display elements of thedisplay; generate, for each of the plurality of display elements, a sumof the EM field contributions from the plurality of primitives to thedisplay element; and generate, for each of the plurality of displayelements, the respective control signal based on the sum of the EM fieldcontributions to the display element.

Another aspect of the present disclosure features a system including: adisplay including a plurality of display elements and any one of theoptical devices as described herein, and the optical device isconfigured to diffract a plurality of different colors of light to thedisplay.

In some implementations, the optical device and the display are arrangedalong a direction. The optical device includes a front surface and aback surface along the direction, and the display includes a frontsurface and a back surface along the direction, and the front surface ofthe display is spaced from the back surface of the optical device.

In some implementations, the front surface of the display is spaced fromthe back surface of the optical device by a gap. At least one of thefront surface of the display or the back surface of the optical devicecan be treated with an anti-reflection coating.

In some implementations, the system further includes a transparentprotective layer on the back surface of the optical device.

In some implementations, the front surface of the display and the backsurface of the optical device are attached together by an intermediatelayer. The intermediate layer can be configured to have a refractiveindex lower than a refractive index of a layer of the optical device,such that each of the plurality of colors of light transmitted at zeroorder by the optical device is totally reflected at an interface betweenthe intermediate layer and the layer of the optical device.

In some implementations, the system further includes a cover (e.g., acover glass) on the front surface of the display, where the opticaldevice is formed in the cover glass.

In some implementations, the optical device is configured to receive theplurality of colors of light at the front surface of the optical device.

In some implementations, the optical device includes a substrate infront of the optical device and is configured to receive the pluralityof colors of light at a side surface of the substrate that is angled toa back surface of the substrate.

In some implementations, the optical device includes at least onediffractive grating supported by the substrate and configured todiffract the plurality of different colors of light towards the display.

In some implementations, the substrate includes a container filled witha liquid having a refractive index smaller than a recording medium ofthe diffractive grating.

In some implementations, the substrate is wedge-shaped and comprises atitled front surface. An angle between the front surface and the sidesurface can be less than 90 degree.

In some implementations, the optical device is configured to receivedifferent portions of the plurality of different colors of light alongdifferent optical paths in the substrate and to diffract the differentportions to illuminate different corresponding regions of the display.The different regions can include two or more of a lower region, anupper region, a left region, and a right region of the display. Thedifferent portions of the plurality of different colors of light can beprovided by different corresponding illuminators. The optical device canbe configured to receive different portions of the plurality ofdifferent colors of light from different corresponding side surfaces ofthe substrate.

In some examples, the optical device is configured to: receive a firstportion of the plurality of different colors of light from a first sidesurface of the substrate to the back surface of the optical device anddiffract the first portion to illuminate a first region of the display,and receive a second portion of the plurality of different colors oflight from a second side surface of the substrate to the front surfaceof the optical device, reflect the second portion back to the backsurface of the optical device, and diffract the second portion toilluminate a second region of the display. The first side surface andthe second side surface can be a same side surface. The second portionof the plurality of different colors of light can be reflected by totalinternal reflection or a reflective grating in the optical device. Thesubstrate can also include a partially reflective surface configured toseparate an input light into the first portion and the second portion.

In some implementations, the optical device includes at least onediffractive grating arranged at the back surface of the optical device.The diffractive grating can include different sub-regions with differentcorresponding diffraction efficiencies. The diffractive grating can beconfigured to: diffract a first portion of the plurality of differentcolors of light incident at a first sub-region of the diffractivegrating to illuminate a first region of the display and reflect a secondportion of the plurality of different colors of light to the front backof the optical device that is further reflected back to the back surfaceof the optical device and incident at a second sub-region of thediffractive grating, and diffract the second portion to illuminate asecond, different region of the display.

In some examples, the diffractive grating is configured such that thediffracted first portion and the diffracted second portion on the firstregion and the second region of the display have a substantially sameoptical power. The first and second regions of the display can havedifferent reflectivities that are associated with first and seconddifferent diffraction efficiencies of the first and second sub-regionsof the diffractive grating.

In some implementations, the diffractive grating includes a plurality ofsub-regions that are tiled together. The sub-regions can be tiled alonga horizontal direction.

In some cases, edges of the different sub-regions are configured to abuteach other in an optically seamless manner. The different sub-regionscan be formed by including one or more edge-defining elements in anoptical path of at least one of a recording beam or an object beamduring recording each sub-region in a recording medium, and the one ormore edge-defining elements can include a square aperture, a rectangularaperture, or a plane-tiling aperture.

In some cases, two adjacent sub-regions of the diffractive grating abutwith a gap. The display can include multiple tiled display devices, andthe gap between the adjacent sub-regions of the diffractive grating isaligned with a gap between adjacent tiled display devices of thedisplay.

In some cases, two adjacent different sub-regions have an overlap.

In some implementations, the diffractive grating is mechanically formedby using an embossed, nano-imprinted, or self-assembled structure.

In some implementations, the display has a width along a horizontaldirection and a height along a vertical direction, both the horizontaldirection and the vertical direction being perpendicular to thedirection, and an aspect ratio between the width and the height can belarger than 16:9.

In some implementations, the optical device is configured to diffract aplurality of different colors of light at respective diffracted anglesthat are substantially identical to each other. In some examples, eachof the respective diffracted angles is in a range of −10 degrees to 10degrees.

In some implementations, the display is configured to diffract thediffracted colors of light back through the optical device.

In some implementations, an area of the optical device covers an area ofthe display.

In some implementations, the system further includes: an illuminatorarranged adjacent to the optical device and configured to provide theplurality of colors of light to the optical device. The illuminator caninclude a plurality of light emitting elements each configured to emit arespective color of light.

In some implementations, centers of beams from the plurality of lightemitting elements can be offset with respect to one another. Theilluminator can be configured to provide a light beam with an ellipticalbeam profile or a rectangular beam profile. The illuminator can beconfigured to provide a light beam with a particular polarizationorientation. The illuminator can include one or more optical componentsconfigured to independently control ellipticity and polarizationorientation of each of the plurality of different colors of light.

In some implementations, the illuminator includes one or more opticalcomponents configured to control a uniformity of the plurality ofdifferent colors of light. The one or more optical components includeapodizing optical elements or profile converters.

In some implementations, the system includes one or more anamorphic orcylindrical optical elements configured to increase a width of theplurality of different colors of light.

In some implementations, the system can further include: a prism elementbetween the illuminator and the optical device and configured to receivethe plurality of different colors of light from an input surface of theprism element; and one or more expansion gratings adjacent an exitsurface of the prism element, each of the one or more expansion gratingsconfigured to expand a beam profile of a different corresponding colorof light by a factor in at least one dimension.

In some implementations, the system can further include: one or morereflectors downstream of the one or more expansion diffractive gratings,each of the one or more reflectors being configured to reflect arespective color of light into the optical device. A tilt angle of eachof the one or more reflectors can be independently adjustable to cause auniformity of diffraction from the optical device to the display.

The system can further include at least one of a color sensor or abrightness sensor configured to detect one or more optical properties ofa holographic light field formed by the system, wherein the tilt anglesof the one or more reflectors are adjustable based on the detectedoptical properties of the holographic light field. The one or moreoptical properties can include brightness uniformity, color uniformity,or white point.

In some implementations, the one or more reflectors are adjustable tocorrect for changes in alignment of components of the system.

In some implementations, an optical distance between the one or morereflectors and the optical device is configured such that each of theplurality of different colors of light is reflected by a correspondingreflector without transmission through one or more other reflectors.

In some implementations, the one or more reflectors are configured sothat light illuminated at each of the one or more reflectors comes froma substantially different direction.

In some implementations, an angle between the prism element and asubstrate of the optical device is adjustable to tilt a position of aholographic light field formed by the system.

In some implementations, the one or more expansion gratings areconfigured to at least partially collimate the plurality of differentcolors of light in one or two traverse directions.

In some implementations, the system further includes: a controllercoupled to the illuminator and configured to control the illuminator toprovide each of the plurality of colors of light. The controller can becoupled to the display and configured to transmit a respective controlsignal to each of the plurality of display elements for modulation of atleast one property of the display element.

In some implementations, the controller is configured to: obtain graphicdata including respective primitive data for a plurality of primitivescorresponding to an object in a three-dimensional space; determine, foreach of the plurality of primitives, an electromagnetic (EM) fieldcontribution to each of the plurality of display elements of thedisplay; generate, for each of the plurality of display elements, a sumof the EM field contributions from the plurality of primitives to thedisplay element; and generate, for each of the plurality of displayelements, the respective control signal based on the sum of the EM fieldcontributions to the display element.

In some implementations, the controller is configured to: sequentiallymodulate the display with information associated with the plurality ofcolors of light in a series of time periods, and control the illuminatorto sequentially emit each of the plurality of colors of light to theoptical device during a respective time period of the series of timeperiods, such that each of the plurality of colors of light isdiffracted by the optical device to the display and reflected bymodulated display elements of the display to form a respective colorthree-dimensional light field corresponding to the object during therespective time period.

In some implementations, the controller is configured to modulate thedisplay such that the respective color three-dimensional light fieldappears fully in front of the display, fully behind the display, orpartially in front of the display and partially behind the display.

In some cases, the display includes a spatial light modulator (SLM)including a digital micro-mirror device (DMD) or a liquid crystal onsilicon (LCOS) device.

In some implementations, the system further includes an opticalpolarizer arranged between the display and the optical device, whereinthe optical polarizer is configured to change a polarization state ofthe plurality of different colors of light.

In some implementations, the optical device includes: an opticaldiffractive component configured to diffract light comprising theplurality of different colors of light to the display that is configuredto diffract a portion of the light illuminating the display elements.

In some implementations, the optical device further includes: anoptically redirecting component configured to transmit the portion ofthe light to form a holographic scene and to redirect display zero orderlight away from the holographic scene in a three-dimensional (3D) space,the display zero order light comprising reflected light from thedisplay.

In some implementations, the optical redirecting component includes aplurality of redirecting holographic grating for the display zero orderlight of the plurality of different colors of light, and each of theplurality of redirecting holographic gratings is configured to diffractdisplay zero order light of a respective color of light of the pluralityof different colors of light at a respective diffractive angle towards arespective direction in the 3D space.

In some implementations, the optical diffractive component is configuredto diffract the plurality of different colors of light to illuminate thedisplay at an angle of about 0°, such that the optical diffractivecomponent redirects the display zero order light reflected from thedisplay away from the holographic scene.

In some implementations, a ratio between an amount of the display zeroorder light in the holographic scene with suppression of the opticaldiffractive component and the optically redirecting component and anamount of the display zero order light in the holographic scene withoutthe suppression is less than 2%.

In some implementations, the optically redirecting component includes aone-dimensional suppression grating, and the holographic scene comprisesa band corresponding to suppression of the display zero order light, andthe system can be configured such that the band is outside of a viewingeyesight of a viewer.

Another aspect of the present disclosure features a system including: adisplay including a plurality of display elements; an optical devicearranged adjacent to the display and configured to diffract light to thedisplay; and a controller coupled to the display and configured to:obtain graphic data including respective primitive data for a pluralityof primitives corresponding to an object in a three-dimensional space;determine, for each of the plurality of primitives, an electromagnetic(EM) field contribution to each of the plurality of display elements ofthe display by calculating, in a three-dimensional coordinate system, anEM field propagation from the primitive to the display element;generate, for each of the plurality of display elements, a sum of the EMfield contributions from the plurality of primitives to the displayelement; and transmit, for each of the plurality of display elements, arespective control signal based on the sum of the EM field contributionsto the display element for modulation of at least one property of thedisplay element.

In some implementations, the optical device can include any one of theoptical devices including at least one color-selective polarizer asdescribe herein.

In some implementations, the optical device includes any one of theoptical devices including at least one reflective layer as describedherein.

In some implementations, the optical device includes a holographicgrating formed in a recording medium.

In some implementations, the optical device includes a plurality ofholographic gratings formed on a recording medium, and each of theplurality of holographic gratings is configured to diffract light with arespective color having a respective incident angle to the display.

In some implementations, the optical device is arranged in front of thedisplay and the display is configured to diffract the diffracted lightback through the optical device to form a three-dimensional light fieldcorresponding to the object.

In some implementations, the system further includes: an illuminatorarranged adjacent to the optical device and configured to provide thelight to the optical device.

In some implementations, the controller is configured to: sequentiallymodulate the display with information associated with a plurality ofcolors corresponding to a plurality of colors of light in a series oftime periods, and control the illuminator to sequentially emit each ofthe plurality of colors of light to the optical device during arespective time period of the series of time periods, such that each ofthe plurality of colors of light is diffracted by the optical device tothe display and reflected by modulated display elements of the displayto form a respective color three-dimensional light field correspondingto the object during the respective time period.

Another aspect of the present disclosure features a method including:making any one of the optical devices as described herein.

Another aspect of the present disclosure features a method of making anyone of the optical devices including at least one color-selectivepolarizer, including: forming the first optically diffractive component;forming the second optically diffractive component; and arranging thecolor-selective polarizer between the first optically diffractivecomponent and the second optically diffractive component.

In some implementations, forming the first optically diffractivecomponent includes: forming a first diffractive structure in a recordingmedium.

In some implementations, forming the first diffractive structure in therecording medium includes: recording a first holographic grating in therecording medium by illuminating a first recording object beam at afirst recording object angle and a first recording reference beam at afirst recording reference angle on the recording medium, where the firstrecording object beam and the first recording reference beam have a samewavelength and the same first polarization state.

In some examples, the first color of light includes a wavelength rangewider than or identical to that of the first recording reference beam orthe first recording object beam. In some examples, the first recordingreference beam corresponds to a color different from a first color ofthe first color of light.

In some examples, the first incident angle of the first color of lightis substantially identical to the first recording reference angle, andthe first diffracted angle is substantially identical to the firstrecording object angle.

In some examples, the first recording reference angle is in a range from70 degrees to 90 degrees. In some examples, the first recordingreference angle is in a range from 80 degrees to 90 degrees. In someexamples, the first recording object angle is in a range from −10degrees to 10 degrees. In some examples, the first recording objectangle is substantially identical to 6 degrees. In some examples, thefirst recording object angle is substantially identical to 0 degrees. Insome examples, a sum of the first recording reference angle and thefirst recording object angle is substantially identical to 90 degrees.

In some implementations, a thickness of the recording medium is morethan one order of magnitude larger than the wavelength of the firstrecording object beam. The thickness of the recording medium can beabout 30 times larger than the wavelength of the first recording objectbeam.

In some implementations, forming the first diffractive structure in therecording medium includes: fixing the first diffractive structure in therecording medium.

In some implementations, the recording medium is between a carrier filmand a diffraction substrate.

In some examples, the first diffracted angle and the second diffractedangle are substantially identical to each other. In some examples, thefirst incident angle and the second incident angle are substantiallyidentical to each other.

In some implementations, arranging the color-selective polarizer betweenthe first optically diffractive component and the second opticallydiffractive component includes: sequentially stacking the firstoptically diffractive component, the color-selective polarizer, and thesecond optically diffractive component, such that the first color oflight and the second color of light are incident on the first opticallydiffractive component before the second optically diffractive component.

In some implementations, sequentially stacking the first opticallydiffractive component, the color-selective polarizer, and the secondoptically diffractive component includes: sequentially arranging thefirst optically diffractive component, the color-selective polarizer,and the second optically diffractive component on a substrate that isbefore the first optically diffractive component.

In some implementations, sequentially stacking the first opticallydiffractive component, the color-selective polarizer, and the secondoptically diffractive component includes: attaching the color-selectivepolarizer to the first optically diffractive component through a firstintermediate layer; and attaching the second optically diffractivecomponent to the color-selective polarizer through a second intermediatelayer, where each of the first and second intermediate layers includes arespective refractive index matching material.

In some implementations, the method further includes: forming a thirdoptically diffractive component configured to diffract a third color oflight having the first polarization state and a third incident angle ata third diffracted angle with a third diffraction efficiency; andarranging a second color-selective polarizer between the second andthird optically diffractive components, where the second color-selectivepolarizer is configured to rotate a polarization state of the thirdcolor of light from the second polarization state to the firstpolarization state.

In some implementations, the color-selective polarizer is configured torotate a polarization state of the first color of light from the firstpolarization state to the second polarization state, and the secondcolor-selective polarizer is configured to rotate the polarization stateof the second color of light from the first polarization state to thesecond polarization state, without rotation of the polarization state ofthe first color of light.

In some implementations, the method further includes: arranging a thirdcolor-selective polarizer sequential to the third optically diffractivecomponent such that the third optically diffractive component is betweenthe second and third color-selective polarizers, where the thirdcolor-selective polarizer is configured to rotate the polarization stateof each of the first and second colors of light from the secondpolarization state to the first polarization state, without rotation ofthe polarization state of the third color of light.

In some implementations, the method further includes: arranging a fourthcolor-selective polarizer before the first optically diffractivecomponent such that the first optically diffractive component is betweenthe fourth color-selective polarizer and the color-selective polarizer,where the fourth color-selective polarizer is configured to rotate apolarization state of the first color of light from the secondpolarization state to the first polarization state, without rotation ofthe polarization state of each of the second and third colors of light.

In some implementations, the first polarization state is s polarization,and the second polarization state is p polarization.

Another aspect of the present disclosure features a method of making anyone of the optical devices including at least one reflective layer,including: forming the first optically diffractive component includingthe first diffractive structure; forming the second opticallydiffractive component including the second diffractive structure;arranging the first reflective layer between the first diffractivestructure and the second diffractive structure, the second diffractivestructure being sequential to the first diffractive structure along adirection; and arranging the second reflective layer sequential to thesecond diffractive structure along the direction.

In some implementations, the method further includes: forming an opticalabsorber on a side surface of the optical device, where the opticalabsorber is configured to absorb the totally reflected light of thefirst and second colors.

In some implementations, the first reflective layer is configured tohave a refractive index smaller than that of a layer of the firstoptically diffractive component that is immediately adjacent to thefirst reflective layer, such that the first color of light having thefirst incident angle is totally reflected by an interface between thefirst reflective layer and the layer of the first optically diffractivecomponent, without totally reflecting the second color of light havingthe second incident angle.

In some implementations, the method further includes: forming a thirdoptically diffractive component including a third diffractive structureconfigured to diffract a third color of light having a third incidentangle, where arranging the second reflective layer sequential to thesecond diffractive structure along the direction includes: arranging thesecond reflective layer between the second diffractive structure and thethird diffractive structure along the direction. Each of the firstreflective layer and the second reflective layer can be configured totransmit the third color of light having the third incident angle.

In some implementations, the method further includes: arranging a thirdreflective layer sequential to the third diffractive structure along thedirection, where the third reflective layer is configured to totallyreflect the third color of light having the third incident angle.

In some implementations, each of the first, second, and third opticallydiffractive components includes a respective carrier film and arespective diffraction substrate, and the first reflective layerincludes a first carrier film of the first optically diffractivecomponent. Arranging the first reflective layer between the firstdiffractive structure and the second diffractive structure can include:attaching a second diffraction substrate of the second opticallydiffractive component to the first carrier film of the first opticallydiffractive component by a first intermediate layer. Arranging thesecond reflective layer between the second diffractive structure and thethird diffractive structure along the direction can include: attaching asecond carrier film of the second optically diffractive component to athird carrier film of the third optically diffractive component by asecond intermediate layer. The second reflective layer can include thesecond intermediate layer. The third reflective layer can be attached toa third diffraction substrate of the third optically diffractivecomponent.

In some implementations, the method further includes: arranging thefirst optically diffractive component on a substrate that is before thefirst optically diffractive component along the direction, where thesubstrate includes a front surface and a back surface.

In some implementations, arranging the first optically diffractivecomponent on the substrate includes: attaching a front surface of thefirst optically diffractive component to the back surface of thesubstrate through a refractive index matching material.

In some implementations, the substrate includes a side surface angled tothe back surface of the substrate, and the substrate is configured toreceive a plurality of different colors of light at the side surface.The substrate can be configured such that the plurality of differentcolors of light are incident on the side surface with an incident anglesubstantially identical to 0 degrees.

In some implementations, forming the first optically diffractivecomponent including the first diffractive structure includes: formingthe first diffractive structure in a recording medium.

In some implementations, forming the first diffractive structure in therecording medium includes: recording a first holographic grating in therecording medium by injecting a first recording object beam at a firstrecording object angle and a first recording reference beam at a firstrecording reference angle, where the first recording object beam and thefirst recording reference beam have a same wavelength and a samepolarization state.

In some implementations, the first color of light includes a wavelengthrange wider than or identical to that of the first recording referencebeam.

In some implementations, the first recording reference beam correspondsto a color different from a first color of the first color of light.

In some implementations, the first incident angle of the first color oflight is substantially identical to the first recording reference angle,and the first diffracted angle is substantially identical to the firstrecording object angle.

In some examples, the first recording reference angle is in a range from70 degrees to 90 degrees. In some examples, the first recordingreference angle is in a range from 70 degrees to 80 degrees. In someexamples, the first recording object angle is in a range from −10degrees to 10 degrees.

In some implementations, a thickness of the recording medium is morethan one order of magnitude larger than the wavelength of the firstrecording object beam. The thickness of the recording medium can beabout 30 times larger than the wavelength of the first recording objectbeam.

In some implementations, forming the first diffractive structure in therecording medium includes: fixing the first diffractive structure in therecording medium.

In some implementations, the first incident angle is different from thesecond incident angle. In some examples, the first color of light has awavelength smaller (or shorter) than the second color of light, and thefirst incident angle is larger (or longer) than the second incidentangle.

Another aspect of the present disclosure features a method including:forming any one of the optical devices as described herein according toany one the methods as described above, and arranging the optical deviceand a display including a plurality of display elements, such that theoptical device is configured to diffract a plurality of different colorsof light to the display.

In some implementations, arranging the optical device and the displayincludes: spacing a back surface of the optical device from a frontsurface of the display by a gap.

In some implementations, the method further include: forming ananti-reflection coating on at least one of the front surface of thedisplay or the back surface of the optical device.

In some implementations, arranging the optical device and the displayincludes: attaching a back surface of the optical device on a frontsurface of the display through an intermediate layer.

In some cases, the intermediate layer is configured to have a refractiveindex lower than a refractive index of a layer of the optical device,such that each of the plurality of different colors of light transmittedat zero order by the optical device is totally reflected at an interfacebetween the intermediate layer and the layer of the optical device.

In some implementations, the optical device is configured to diffractthe plurality of different colors of light at respective diffractedangles that are substantially identical to each other.

In some examples, each of the respective diffracted angles is in a rangeof −10 degrees to 10 degrees.

In some implementations, the display is configured to diffract thediffracted colors of light back through the optical device.

In some implementations, an area of the optical device covers an area ofthe display.

In some implementations, the optical device includes a substrate infront of the optical device and is configured to receive the pluralityof different colors of light at a side surface of the substrate that isangled to a back surface of the substrate.

Another aspect of the present disclosure features a method including:using an optical device to convert an incoming beam including aplurality of different colors of light to individually diffracted colorsof light. The optical device can be any one of the optical devices asdescribed herein.

Another aspect of the present disclosure features a method including:transmitting at least one timing control signal to an illuminator toactivate the illuminator to emit a plurality of different colors oflight onto an optical device, such that the optical device converts theplurality of different colors of light to individually diffracted colorsof light to illuminate a display including a plurality of displayelements, where the optical device is any one of the optical devices asdescribed herein; and transmitting, for each of the plurality of displayelements of the display, at least one respective control signal tomodulate the display element, such that the individually diffractedcolors of light are reflected by the modulated display elements to forma multi-color three-dimensional light field corresponding to therespective control signals.

In some implementations, the method further includes: obtaining graphicdata including respective primitive data for a plurality of primitivescorresponding to an object in a three-dimensional space; determining,for each of the plurality of primitives, an electromagnetic (EM) fieldcontribution to each of the plurality of display elements of the displayby calculating, in a three-dimensional coordinate system, an EM fieldpropagation from the primitive to the display element; generating, foreach of the plurality of display elements, a sum of the EM fieldcontributions from the plurality of primitives to the display element;and generating, for each of the plurality of display elements, therespective control signal based on the sum of the EM field contributionsto the display element for modulation of at least one property of thedisplay element, where the multi-color three-dimensional light fieldcorresponds to the object.

In some implementations, the method includes: sequentially modulatingthe display with information associated with the plurality of differentcolors in a series of time periods, and controlling the illuminator tosequentially emit each of the plurality of different colors of light tothe optical device during a respective time period of the series of timeperiods, such that each of the plurality of different colors of light isdiffracted by the optical device to the display and reflected by themodulated display elements of the display to form a respective colorthree-dimensional light field corresponding to the object during therespective time period.

In some implementations, the plurality of different colors of light arediffracted by the optical device at a substantially same diffractedangle to the display. In some examples, the diffracted angle is within arange from −10 degrees to 10 degrees.

In some implementations, the illuminator and the optical device areconfigured such that the plurality of different colors of light areincident on the first optically diffractive component of the opticaldevice with respective incident angles. In some examples, the respectiveincident angles are different from each other. In some examples, therespective incident angles are substantially identical to each other. Insome examples, each of the respective incident angles is in a range from70 degrees to 90 degrees.

Another aspect of the present disclosure features an optical device,including: at least two optically diffractive components and at leastone color-selective polarizer, where the optical device is configuredsuch that, when light of different colors is incident on the opticaldevice, the optical device separates light of individual colors of thedifferent colors while suppressing crosstalk between the differentcolors.

In some implementations, the optical device is configured such that,when the light of different colors is incident on the optical device,each of the optically diffractive components diffracts light of arespective color of the different colors.

In some implementations, the optical device is configured such that, inan output light beam diffracted by the optical device, a power of lightof a particular color of the different colors is at least one order ofmagnitude higher than a power of light of one or more other colors ofthe different colors.

In some implementations, the at least one color-selective polarizer isconfigured to rotate a polarization state of light of at least one colorof the different colors, such that light of a particular color of thedifferent colors is incident in a first polarization state on arespective one of the optically diffractive components, while light ofone or more other colors of the different colors is incident in a secondpolarization state different from the first polarization state on therespective one of the optically diffractive components.

Another aspect of the present disclosure features an optical device,including: at least two optically diffractive components and at leastone reflective layer, where the optical device is configured such that,when light of different colors is incident on the optical device, theoptical device separates light of individual colors of the differentcolors while suppressing crosstalk between the different colors, andwhere the at least one reflective layer is configured for total internalreflection of light of at least one of the different colors.

In some implementations, the optical device is configured such that anoutput light beam diffracted by the optical device includes only lightof a particular color of the different colors without crosstalk from oneor more other colors of the different colors.

In some implementations, the at least one reflective layer is configuredto totally reflect zero order light of a particular color of thedifferent colors transmitted by a respective one of the opticallydiffractive component, while transmitting one or more other colors ofthe different colors

In some implementations, the optical device is configured such that,when the light of different colors is incident on the optical device,each of the optically diffractive components diffracts light of arespective color of the different colors.

Another aspect of the present disclosure features a display and any oneof the optical devices as described herein, where the optical device isconfigured to diffract a plurality of different colors of light to thedisplay.

Another aspect of the present disclosure features an illuminatorconfigured to provide a plurality of different colors of light and anyone of the optical devices as described herein, where the optical deviceis configured to diffract the plurality of different colors of lightfrom the illuminator.

Another aspect of the present disclosure features a system including: adisplay and an optical device including one or more transmissivediffractive structures for diffracting light to the display.

In some implementations, the display is a reflective display configuredto diffract the light back through the optical device. In someimplementations, the system further includes an illuminator configuredto provide the light to the optical device, where the illuminator isarranged in a front side of the transmissive diffractive structures ofthe optical device.

In some implementations, the display is a transmissive displayconfigured to diffract the light forwards through the optical device. Insome implementations, the system further includes an illuminatorconfigured to provide the light to the optical device, where theilluminator is arranged in a rear side of the transmissive diffractivestructures of the optical device.

In some implementations, each of the one or more transmissivediffractive structures is configured to diffract a respective color of aplurality of different colors.

In some implementations, the optical device further includes one or morereflective diffractive structures, and each of the one or moretransmissive diffractive structures and the one or more reflectivediffractive structures is configured to diffract a respective color of aplurality of different colors.

Another aspect of the present disclosure features a system including: adisplay and an optical device including one or more reflectivediffractive structures for diffracting light to the display.

In some implementations, the display is a reflective display configuredto diffract the light back through the optical device. In someimplementations, the system further includes an illuminator configuredto provide the light to the optical device, where the illuminator isarranged in a rear side of the reflective diffractive structures of theoptical device.

In some implementations, the display is a transmissive displayconfigured to diffract the light forwards through the optical device. Insome implementations, the system further includes an illuminatorconfigured to provide the light to the optical device, where theilluminator is arranged in a front side of the reflective diffractivestructures of the optical device.

In some implementations, each of the one or more reflective diffractivestructures is configured to diffract a respective color of a pluralityof different colors.

In some implementations, the optical device further includes one or moretransmissive diffractive structures, and each of the one or moretransmissive diffractive structures and the one or more reflectivediffractive structures is configured to diffract a respective color of aplurality of different colors.

Another aspect of the present disclosure features an optical device,including: a plurality of optically diffractive components including atleast one transmissive diffractive structure and at least one reflectivediffractive structure, where the optical device is configured such that,when light of different colors is incident on the optical device, theoptical device separates light of individual colors of the differentcolors while suppressing crosstalk between the different colors.

In some implementations, each of the transmissive diffractive structureand the reflective diffractive structure is configured to light of arespective color of the different colors.

In some implementations, the optical device further includes: at leastone reflective layer configured for total internal reflection of lightof at least one of the different colors.

In some implementations, the optical device further includes: at leastone color-selective polarizer configured to rotate a polarization stateof light of at least one color of the different colors, such that lightof a particular color of the different colors is incident in a firstpolarization state on a respective one of the optically diffractivecomponents, while light of one or more other colors of the differentcolors is incident in a second polarization state different from thefirst polarization state on the respective one of the opticallydiffractive components.

Another aspect of the present disclosure features a system including: adisplay and an optical device according to any one of the opticaldevices as described herein, where the optical device is configured todiffract a plurality of different colors of light to the display.

Another aspect of the present disclosure features a system including: anilluminator configured to provide a plurality of different colors oflight and an optical device according to any one of the optical devicesas described herein, where the optical device is configured to diffractthe plurality of different colors of light from the illuminator.

In the present disclosure herein, the term “primitive” refers to a basicnondivisible element for input or output within a computing system. Theelement can be a geometric element or a graphical element. The term“hologram” refers to a pattern displayed by (or uploaded to) a displaywhich contains amplitude information or phase information, or somecombination thereof, regarding an object. The term “holographicreconstruction” refers to a volumetric light field (e.g., a holographiclight field) from a display when illuminated.

The details of one or more implementations of the subject matter of thisspecification are set forth in the accompanying drawings and associateddescription. Other features, aspects, and advantages of the subjectmatter will become apparent from the description, the drawings, and theclaims.

It is to be understood that various aspects of implementations can becombined in different manners. As an example, features from certainmethods, devices, or systems can be combined with features of othermethods, devices, or systems.

DESCRIPTION OF DRAWINGS

FIG. 1A illustrates a schematic diagram of an example system including aholographic display.

FIG. 1B illustrates a schematic diagram of an example holographicdisplay.

FIG. 1C illustrates an example system for 3D displays.

FIG. 2 illustrates an example configuration for electromagnetic (EM)propagation calculation.

FIG. 3A illustrates an example EM propagation for a point primitiverelative to an element of a display.

FIG. 3B illustrates an example EM propagation for a line primitiverelative to an element of a display.

FIG. 3C illustrates an example EM propagation for a triangle primitiverelative to an element of a display.

FIG. 3D illustrates an example implementation of Maxwell holographicocclusion for a point primitive with a line primitive as an occluder.

FIG. 3E illustrates an example implementation of Maxwell holographicocclusion for a line primitive with another line primitive as anoccluder.

FIG. 3F illustrates an example implementation of Maxwell holographicocclusion for a triangle primitive with a line primitive as an occluder.

FIG. 3G illustrates an example implementation of Maxwell holographicstitching.

FIG. 4 is a flowchart of an example process of displaying an object in3D.

FIG. 5A illustrates an example system for 3D display including areflective display with front illumination.

FIG. 5B illustrates another example system for 3D display including areflective display with front illumination.

FIG. 5C illustrates another example system for 3D display including atransmissive display with back illumination.

FIG. 5D illustrates another example system for 3D display including atransmissive display with waveguide illumination.

FIG. 5E illustrates another example system for 3D display including atransmissive display with waveguide illumination.

FIG. 5F illustrates another example system for 3D display including areflective display with waveguide illumination.

FIG. 5G illustrates another example system for 3D display including areflective display with waveguide illumination.

FIG. 5H illustrates another example system for 3D display including areflective display with optically diffractive illumination using atransmissive field grating based structure.

FIG. 5I illustrates another example system for 3D display including areflective display with optically diffractive illumination using areflective field grating based structure.

FIG. 5J illustrates another example system for 3D display including atransmissive display with optically diffractive illumination using areflective field grating based structure.

FIG. 5K illustrates another example system for 3D display including atransmissive display with optically diffractive illumination using atransmissive field grating based structure.

FIG. 6A illustrates an example display with display elements havingnonuniform shapes.

FIG. 6B illustrates an example display with display elements havingdifferent sizes.

FIG. 7A illustrates an example of recording a grating in a recordingmedium.

FIG. 7B illustrates an example of diffracting a replay reference beam bythe grating of FIG. 7A.

FIG. 7C illustrates an example of recording gratings for differentcolors in a recording medium using different colors of light.

FIG. 7D illustrates an example of recording gratings for differentcolors in a recording medium using a same color of light.

FIG. 7E illustrates an example of diffracting replay reference beams ofdifferent colors by gratings for different colors.

FIG. 7F illustrates an example of crosstalk among diffracted beams ofdifferent colors.

FIG. 8 illustrates an example of recording a diffractive grating with alarge reference angle in a recording medium.

FIG. 9A illustrates an example optical device, including diffractivegratings for two colors and corresponding color-selective polarizers,for individually diffracting the two colors of light.

FIG. 9B illustrates an example of diffracting the two colors of light bythe optical device of FIG. 9A.

FIG. 10A illustrates an example optical device, including diffractivegratings for three colors and corresponding color-selective polarizers,for individually diffracting the three colors of light.

FIG. 10B illustrates an example of diffracting the three colors of lightby the optical device of FIG. 10A.

FIG. 11 illustrates an example optical device, including diffractivegratings for two colors and corresponding reflective layers, forindividually diffracting the two colors of light.

FIG. 12A illustrates an example optical device, including diffractivegratings for three colors and corresponding reflective layers, forindividually diffracting the three colors of light.

FIG. 12B illustrates another example optical device includingdiffractive gratings for three colors and corresponding reflectivelayers with a wedged substrate.

FIG. 12C illustrates a further example optical device includingdiffractive gratings for three colors and corresponding reflectivelayers with a wedged input face.

FIGS. 13A-13C illustrate relationships between diffracted and reflectedbeam power with different incident angles for a blue color of light(FIG. 13A), a green color of light (FIG. 13B), and a red color of light(FIG. 13C).

FIG. 14A is a flowchart of an example process of fabricating an opticaldevice including holographic gratings and corresponding color-selectivepolarizers.

FIG. 14B is a flowchart of an example process of fabricating an opticaldevice including holographic gratings and corresponding reflectivelayers.

FIG. 15 illustrates an example optical device including a combination oftransmissive and reflective diffractive gratings.

FIG. 16 illustrates an example of incident light being diffracted bydisplay elements of a display and reflected at gaps between the displayelements on the display.

FIG. 17A illustrates an example of display zero order light within aholographic scene displayed on a projection screen.

FIG. 17B illustrates an example of display zero order light within aholographic scene displayed on a viewer's eye.

FIG. 18 illustrates an example of suppressing display zero order lightin a holographic scene displayed on a projection screen by diverging thedisplay zero order light.

FIG. 19A illustrates an example of display zero order light in aholographic scene when the display is illuminated with light at normalincidence.

FIG. 19B illustrates an example of suppressing display zero order lightin a holographic scene displayed on a projection screen by directing thedisplay zero order light away from the holographic scene when thedisplay is illuminated with light at an incident angle.

FIG. 19C illustrates an example of suppressing display zero order lightin a holographic scene displayed on a viewer's eye by directing thedisplay zero order light away from the holographic scene when thedisplay is illuminated with light at an incident angle.

FIG. 20A illustrates an example of a configuration cone and areconstruction cone corresponding to a holographic scene with respect toa display in a 3D coordinate system.

FIG. 20B illustrates an example of adjusting the configuration cone ofFIG. 20A to configure a hologram corresponding to the holographic scenein the 3D coordinate system.

FIG. 21 illustrates an example of coupling light via a coupling prism toan optically diffractive device to illuminate a display at an incidentangle for suppressing display zero order light in a holographic scene.

FIG. 22 illustrates an example of coupling light via a wedged substrateto an optically diffractive device to illuminate a display at anincident angle for suppressing display zero order light in a holographicscene.

FIG. 23A illustrates an example of suppressing display zero order lightin a holographic scene displayed on a projection screen by absorbing thedisplay zero order light reflected from the display with a metamateriallayer.

FIG. 23B illustrates an example of suppressing display zero order lightin a holographic scene displayed on a viewer's eye by blocking (orabsorbing) the display zero order light reflected from the display witha metamaterial layer.

FIG. 24 illustrates a system of suppressing display zero order light ina holographic scene by redirecting the display zero order light awayfrom the holographic scene via an optically redirecting structure.

FIGS. 25A-25C illustrate examples of redirecting display zero orderlight via optically redirecting structures to different directions inspace.

FIGS. 26A-26E illustrate examples of redirecting display zero orderlight when light is input at different incident angles via opticallyredirecting structures to different directions in space.

FIG. 27A illustrates an example of redirecting display zero order lightwith p polarization to transmit at a Brewster's angle.

FIGS. 27B-27C illustrate examples of redirecting display zero orderlight with s polarization with an optical retarder for transmission at aBrewster's angle.

FIG. 28 illustrates an example of redirecting display zero order lightto an anisotropic transmitter for absorbing the display zero orderlight.

FIG. 29 illustrates an example of redirecting display zero order lightto totally reflect the display zero order light.

FIGS. 30A-30B illustrate examples of redirecting two different colors ofdisplay zero order light to different directions away from a holographicscene.

FIGS. 31A-31B illustrate examples of redirecting three different colorsof display zero order light to different directions away from aholographic scene in a same plane.

FIG. 32 illustrates an example of redirecting three different colors ofdisplay zero order light to different directions away from a holographicscene in space.

FIG. 33 illustrates an example of redirecting three different colors ofdisplay zero order light to different directions away from a holographicscene using a switchable grating for one of the colors.

FIG. 34 is a flowchart of an example process of suppressing display zeroorder light in a holographic scene.

FIGS. 35A-35C illustrate an example of a system for displayingreconstructed 3D objects.

FIGS. 36A-36C illustrate the same views of the system of FIGS. 35A-35C,respectively, but with three colors of light propagate in the system.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

Implementations of the present disclosure feature technologies forenabling 3D displays of complex computer-generated scenes as genuineholograms. The technologies provide a novel and deterministic solutionto real time dynamic computational holography based upon Maxwell'sEquations for electromagnetic fields, which can be represented asMaxwell holography. The calculation (or computation) in Maxwellholography can be represented as Maxwell holographic calculation (orMaxwell holographic computation). In embodiments, the disclosureapproaches a hologram as a Dirichlet or Cauchy boundary conditionproblem for a general electric field, utilizing tools including fieldtheory, topology, analytic continuation, and/or symmetry groups, whichenables to solve for holograms in real time without the limitations oflegacy holographic systems. In embodiments, the technologies can be usedto make phase-only, amplitude-only, or phase-and-amplitude holograms,utilizing spatial light modulators (SLMs) or any other holographicdevices.

Implementations of the present disclosure can provide: 1) a mechanism ofapproximation of a hologram as an electromagnetic boundary condition,using field theory and contact geometry, instead of classic optics; 2)derivation and implementation into computer codes and applicationprogramming interfaces (APIs) of the electromagnetic boundary conditionapproach to computational holography, that is, implementation of thehologram calculation as a 2D analytic function on a plane of thehologram and subsequent discretization into parallel algorithms; and/or3) implementation of a complete set of fully 3D, holographic versions ofstandard computer graphics primitives (e.g., point, line, triangle, andtexture triangle), which can enable full compatibility with standardexisting computer graphics tools and techniques. The technologies canenable devices to display general existing content that is notspecifically created for holography, and simultaneously allows existingcontent creators to create holographic works without having to learnspecial techniques, or use special tools.

Particularly, the technologies disclosed herein can involve the use of amathematical formulation (or expression) of light as an electromagnetic(EM) phenomenon in lieu of the mathematical formulation of classicaloptics that is commonly used in computational holography, e.g., theGerchberg-Saxton (G-S) algorithm. The mathematical formulation disclosedherein is derived from Maxwell's Equations. In embodiments, thetechnologies disclosed herein involve treating the displayed image as anelectromagnetic field and treating a hologram as a boundary valuecondition that produces the electromagnetic field (e.g., a Dirichletproblem). Additionally, a desired image can be constructed using aprimitive paradigm ubiquitous in computer graphics, allowing, forexample, the technologies to be used to display any 3D imagery as aholographic reconstruction, e.g., a holographic light field, instead ofas a projective image on a 2D screen. Compared to depth point cloudstechnologies that suffer from bandwidth limitations, the technologiescan avoid these limitations and use any suitable types of primitives,e.g., a point primitive, a line primitive, or a polygon primitive suchas a triangle primitive. Moreover, the primitives can be rendered withcolor information, texture information, and/or shading information. Thiscan help achieve a recording and compression scheme for CG holographiccontent including holographic videos.

In embodiments, the technologies disclosed herein use Maxwell'sEquations to compute generated holograms as a boundary condition problemfor modeling an electromagnetic field, which can remove dependency onthe fast Fourier transform (FFT) and its inherent limitations, removedependency on collimated light sources such as lasers or light emittingdiodes (LEDs), and/or remove limitations of previous approaches tocomputational holography and non-deterministic solutions.

In embodiments, the technologies disclosed herein can be optimized forcomputational simplicity and speed through a mathematical optimizationprocess that constrains independent inputs to a surface of the hologram,depending on parameters of computer-generated (CG) primitives needed tobuild the scene. This allows work to be performed in a highly paralleland highly optimal fashion in computing architectures, e.g., applicationspecific integrated circuits (ASIC) and multicore architectures. Theprocess of computing the hologram can be considered as a singleinstruction that executes on input data in a form of acomputer-generated imagery (CGI) scene, and can theoretically becompleted in a single clock cycle per CGI primitive.

In embodiments, the technologies disclosed herein treat a holographicscene as an assembly of fully 3D holographic primitive apertures whichare functionally compatible with the standard primitives of conventional3D graphics as employed in, for example, video games, movies,television, computer displays, or any other display technologies. Thetechnologies can enable efficient implementation of these apertureprimitives in hardware and software without limitations inherent instandard implementations of computational holography. Amplitude andcolor of the primitives can be automatically computed. Computationalcomplexity can increase linearly with phase element number n, comparedto n{circumflex over ( )}2 or n*log(n) in standard computationalholography. The images created are fully 3D and not an assemblage ofplanar images, and the technologies do not require iterative amplitudecorrection with unknown numbers of steps. Moreover, the generatedholograms do not have “conjugate” images that take up space on theholographic device.

As the holographic primitives are part of a special collection ofmathematical objects, they can be relatively simple and relatively fastto compute, and they can be uniquely suited to parallel, distributedcomputing approaches. The computability and parallelism can allow forinteractive computation of large holograms to design large areaholographic devices of theoretically unlimited size, which can act asholographic computer displays, phone displays, home theaters, and evenholographic rooms. Moreover, the holograms can fill large areas withlight, e.g., rendering large shaded areas in 3D, without limitationsassociated with conventional holographic computation methods which cancause elements to appear in outline instead of solid. Furthermore, therelatively simple and relatively fast computation allows for the displayof real-time holograms at interactive speeds that are not constrained byn{circumflex over ( )}2 computational load and by iterative amplitudecorrection.

In embodiments, the technologies can realize natural computability onmodern ASIC and multicore architectures and can realize completecompatibility with modern graphics hardware, modern graphics software,and/or modern graphics tools and tool chains. For example, thetechnologies can implement clear and simple holographic APIs and enablehigh performance rendering of arbitrary CG models using conventional 3Dcontent creation tools, e.g., 3ds Max®, SOLIDWORKS®, Maya®, or Unity,through the APIs. The APIs can enable developers or users to interactwith a holographic device, e.g., a light modulator or holographicsystem. The holographic APIs can create computer graphics primitives asdiscrete holographic scene primitives, allowing for rich holographiccontent generation utilizing general purpose and specially designedholographic computation hardware. The creation of a mathematical andcomputational architecture can allow holograms to be rendered using thetools and techniques used to make conventional 3D content and softwareapplications. The optimization of the mathematical and computationalarchitecture can allow for performant embodiments of conventionalgraphics and renderings to be displayed as holographic reconstructions.

Algorithms in the technologies disclosed herein are relatively simple toimplement in hardware. This not only allows the computational speedsneeded for high quality rendering that users expect, but it also allowsthe algorithms to be implemented in relatively simple circuits, e.g.,ASIC gate structures, as part of a holographic device. Accordingly,bandwidth issues that can plague high density displays can becomeirrelevant, as computation of scenes can be spread across the computingarchitecture built into the display device (e.g., built-in-computation)instead of having to be computed remotely and then written to eachdisplay element (or display pixel) of the display for each frame ofcontent. It also means that the number of display elements, and thus thesize of a holographic display, can be relatively unbounded byconstraints that severely limit other technologies.

The technologies disclosed herein can enable multiple interactivetechnologies using structured light to be implemented relatively simplyand relatively inexpensively in different applications, including, forexample, solid-state light detection and ranging (LIDAR) devices, 3Dprinting and machining, smart illuminators, smart microdisplays, opticalswitching, optical tweezers, or any other applications demandingstructured light. The technologies disclosed herein can be also used foroptical simulations, e.g., for grating simulations.

FIG. 1A illustrates a schematic diagram of an example system 100 for 3Ddisplays. The system 100 includes a computing device 102 and aholographic display device (or a Maxwell holographic display device)110. The computing device 102 is configured to prepare data for a listof primitives corresponding to an object, e.g., a 3D object, andtransmit the data to the holographic display device 110 via a wired orwireless connection, e.g., USB-C connection or any other high speedserial connection. The holographic display device 110 is configured tocompute electromagnetic (EM) field contributions from the list ofprimitives to display elements of a display (e.g., a modulator) in theholographic display device 110, modulate the display elements with apattern, e.g., a hologram, based on the computed EM field contributionson the display, and display upon illumination a light fieldcorresponding to the object in 3D, e.g., a holographic reconstruction.Herein, the hologram refers to the pattern displayed on the displaywhich contains amplitude information or phase information, or somecombination thereof, regarding the object. The holographicreconstruction refers to a volumetric light field (e.g., a holographiclight field) from the display when illuminated.

The computing device 102 can be any appropriate type of device, e.g., adesktop computer, a personal computer, a notebook, a tablet computingdevice, a personal digital assistant (PDA), a network appliance, a smartmobile phone, a smartwatch, an enhanced general packet radio service(EGPRS) mobile phone, a media player, a navigation device, an emaildevice, a game console, or any appropriate combination of any two ormore of these computing devices or other computing devices.

The computing device 102 includes an operating system (OS) 104 that caninclude a number of applications 106 as graphics engines. Theapplications 106 can process or render a scene, e.g., any arbitrary CGmodel using standard 3D content creation tools, e.g., 3ds Max®,SOLIDWORKS®, Maya®, or Unity. The scene can correspond to one or morereal or imaginary 3D objects or a representation of objects. Theapplications 106 can operate in parallel to render the scene to obtainan OS graphics abstraction 101 which can be provided to a graphicsprocessing unit (GPU) 108 for further processing. In someimplementations, the OS graphics abstraction 101 is provided to theholographic display device 110 for further processing.

The GPU 108 can include a specialized electronic circuit designed forrapid manipulation of computer graphics and image processing. The GPU108 can process the graphics abstraction 101 of the scene to getprocessed scene data 103 which can be used to obtain a list ofprimitives 105, e.g., indexed in a particular order. The primitives caninclude at least one of a point primitive, a line primitive, or apolygon primitive. In some implementations, the GPU 108 includes a videodriver configured to generate the processed scene data 103 and the listof primitives 105.

In some implementations, the GPU 108 includes a conventional renderer120, by which the list of primitives 105 can be rendered by conventionalrendering techniques, e.g., culling and clipping, into a list of itemsto draw on a conventional monitor 124, e.g., a 2D display screen. Thelist of items can be sent via a screen buffer 122 to the conventionalmonitor 124.

In some implementations, the GPU 108 includes a holographic renderer 130to render the list of primitives 105 into graphic data to be displayedby the holographic display device 110. The graphic data can include thelist of primitives and corresponding primitive data. For example, thegraphic data can include a hex code for each primitive.

In some implementations, the GPU 108 includes both the conventionalrenderer 120 and the holographic renderer 130. In some implementations,the GPU 108 includes the conventional renderer 120 and the holographicdisplay device 110 includes the holographic renderer 130.

The corresponding primitive data for a primitive can also include colorinformation (e.g., a textured color, a gradient color or both), textureinformation, and/or shading information. The shading information can beobtained by any customary CGI surface shading method that involvesmodulating color or brightness of a surface of the primitive.

The primitive data of a primitive can include coordinate information ofthe primitive in a 3D coordinate system, e.g., Cartesian coordinatesystem XYZ, polar coordinate system, cylindrical coordinate system, andspherical coordinate system. As discussed with further detail below, thedisplay elements in the holographic display device 110 can also havecorresponding coordinate information in the 3D coordinate system. Theprimitives at coordinate locations can represent a 3D object adjacent tothe display elements, e.g., in front of the display elements, behind thedisplay elements, or straddling the display elements.

As an example, the primitive is a shaded line, e.g., a straight linethat changes smoothly from one color to another across its span. Theprimitive needs four elements of data to be rendered: two end points,and color information (e.g., a RGB color value) at each end point.Assume that a hex code for the line is a0, and the line stretches from afirst end point (0.1, 0.1, 0.1) to a second end point (0.2, 0.2, 0.2) inthe 3D coordinate system, with the color ½ Blue:RGB=(0,0,128) at thefirst end point and the color full Red:RGB=(255,0,0) at the second endpoint. The holographic renderer determines how much and what kind ofdata to expect for each primitive. For the line, the primitive data forthe shaded line in the primitive stream can be a set of instructions asbelow:

  0xa0  // hex code for the shaded line 0x3dcccccd // first vertex at(0.1, 0.1, 0.1) float (single) 0x3dcccccd 0x3dcccccd 0x000080  // firstvertex color is (0, 0, 128) 0x3e4ccccd // second vertex at (0.2, 0.2,0.2) float (single) 0x3e4ccccd 0x3e4ccccd 0xff0000  // second vertexcolor is (255, 0, 0)

There are a total of 31 hex words in the primitive data for the shadedline primitive. It can be an extremely efficient way to transmit acomplex scene, and the primitive data can further be compressed. Sinceeach primitive is a deterministic Turing step, there is no need forterminators. Different from a traditional model where this lineprimitive is simply drawn on a 2D display screen, the primitive data forthe line is transmitted to the holographic display device 110 that cancompute a hologram and display a corresponding holographicreconstruction presenting a line floating in space.

In some implementations, the computing device 102 transmitsnon-primitive based data, e.g., a recorded light field video, to theholographic display device 110. The holographic display device 110 cancompute sequential holograms to display the video as sequentialholographic reconstructions in space. In some implementations, thecomputing device 102 transmits CG holographic content simultaneouslywith live holographic content to the holographic display device 110. Theholographic display device 110 can also compute corresponding hologramsto display the contents as corresponding holographic reconstructions.

As illustrated in FIG. 1A, the holographic display device 110 includes acontroller 112 and a display 114. The controller 112 can include anumber of computing units or processing units. In some implementations,the controller 112 includes ASIC, field programmable gate array (FPGA)or GPU units, or any combination thereof. In some implementations, thecontroller 112 includes the holographic renderer 130 to render the listof primitives 105 into the graphic data to be computed by the computingunits. In some implementations, the controller 112 receives the OSgraphics abstraction 101 from the computing device 102 for furtherprocessing. The display 114 can include a number of display elements. Insome implementations, the display 114 includes a spatial light modulator(SLM). The SLM can be a phase SLM, an amplitude SLM, or a phase andamplitude SLM. In some examples, the display 114 is a digitalmicro-mirror device (DMD) or a liquid crystal on silicon (LCOS) device.In some implementations, the holographic display device 110 includes anilluminator 116 adjacent to the display 114 and configured to emit lighttoward the display 114. The illuminator 116 can include one or morecoherent light sources, e.g., lasers, one or more semi-coherent lightsources, e.g., LEDs (light emitting diodes) or superluminescent diodes(SLEDs), one or more incoherent light sources, or a combination of suchsources.

Different from a conventional 3D graphics system, which takes a 3D sceneand renders it on to a 2D display device, the holographic display device110 is configured to produce a 3D output such as a holographicreconstruction 117 in a form of a light field, e.g., a 3D volume oflight. In a hologram, each display element can contribute to every partof the holographic reconstruction of the scene. Hence, for theholographic display device 110, each display element potentially needsto be modulated for every part of the scene, e.g., each primitive in thelist of primitives generated by the GPU 108, for complete holographicreproduction of the scene. In some implementations, modulation ofcertain elements can be omitted or simplified based on, for example, anacceptable level of accuracy in the reproduced scene or in some regionof the scene.

In some implementations, the controller 112 is configured to compute anEM field contribution, e.g., phase, amplitude, or both, from eachprimitive to each display element, and generate, for each displayelement, a sum of the EM field contributions from the list of primitivesto the display element. This can be done either by running through everyprimitive and accruing its contribution to a given display element, orby running through each display element for each primitive, or by ahybrid blend of these two techniques.

The controller 112 can compute the EM field contribution from eachprimitive to each display element based on a predetermined expressionfor the primitive. Different primitives can have correspondingexpressions. In some cases, the predetermined expression is an analyticexpression, as discussed with further detail below in relation to FIGS.3A-3C. In some cases, the predetermined expression is determined bysolving Maxwell's Equations with a boundary condition defined at thedisplay 114. The boundary condition can include a Dirichlet boundarycondition or a Cauchy boundary condition. Then, the display element canbe modulated based on the sum of the EM field contributions, e.g., bymodulating at least one of a refractive index, an amplitude index, abirefringence, or a retardance of the display element.

If values of an EM field, e.g., a solution to the Maxwell Equations, ateach point on a surface that bounds the field are known, an exact,unique configuration of the EM field inside a volume bounded by aboundary surface can be determined. The list of primitives (or aholographic reconstruction of a corresponding hologram) and the display114 define a 3D space, and a surface of the display 114 forms a portionof a boundary surface of the 3D space. By setting EM field states (e.g.,phase or amplitude or phase and amplitude states) on the surface of thedisplay 114, for example, by illuminating light on the display surface,the boundary condition of the EM field can be determined. Due to timesymmetry of the Maxwell Equations, as the display elements are modulatedbased on the EM field contributions from the primitives corresponding tothe hologram, a volumetric light field corresponding to the hologram canbe obtained as the holographic reconstruction.

For example, a line primitive of illumination at a specific color can beset in front of the display 114. As discussed in further detail belowwith respect to FIG. 3B, an analytic expression for a linear aperturecan be written as a function in space. Then the EM field contributionfrom the line primitive on a boundary surface including the display 114can be determined. If EM field values corresponding to the computed EMfield contribution are set in the display 114, due to time-symmetry ofthe Maxwell Equations, the same linear aperture used in the computationcan appear at a corresponding location, e.g., a coordinate position ofthe linear primitive in the 3D coordinate system and with the specificcolor.

In some examples, as discussed in further detail below with respect toFIG. 3B, suppose that there is a line of light between two points A andB in the 3D space. The light is evenly lit and has an intensity I perline distance l. At each infinitesimal dl along the line from A to B, anamount of light proportional to I*dl is emitted. The infinitesimal dlacts as a delta (point) source, and the EM field contribution from theinfinitesimal dl to any point on a boundary surface around a scenecorresponding to a list of primitives can be determined. Thus, for anydisplay element of the display 114, an analytic equation that representsthe EM field contribution at the display element from the infinitesimalsegment of the line can be determined. A special kind ofsummation/integral that marches along the line and accrues the EM fieldcontribution of the entire line to the EM field at the display elementof the display can be determined as an expression. Values correspondingto the expression can be set at the display element, e.g., by modulatingthe display element and illuminating the display element. Then, throughtime reversal and a correction constant, the line can be created in thesame location defined by points A and B in the 3D space.

In some implementations, the controller 112 is coupled to the display114 through a memory buffer. The control signal 112 can generate arespective control signal based on the sum of the EM field contributionsto each of the display elements. The control signal is for modulatingthe display element based on the sum of the EM field contributions. Therespective control signals are transmitted to the corresponding displayelements via the memory buffer.

In some implementations, the controller 112 is integrated with thedisplay 114 and locally coupled to the display 114. As discussed withfurther detail in relation to FIG. 1B, the controller 112 can include anumber of computing units each coupled to one or more respective displayelements and configured to transmit a respective control signal to eachof the one or more respective display elements. Each computing unit canbe configured to perform computations on one or more primitives of thelist of primitives. The computing units can operate in parallel.

In some implementations, the illuminator 116 is coupled to thecontroller 112 and configured to be turned on/off based on a controlsignal from the controller 112. For example, the controller 112 canactivate the illuminator 116 to turn on in response to the controller112 completing the computation, e.g., all the sums of the EM fieldcontributions for the display elements are obtained. As noted above,when the illuminator 116 emits light on the display 114, the modulatedelements of the display cause the light to propagate in differentdirections to form a volumetric light field corresponding to the list ofprimitives that correspond to the 3D object. The resulting volumetriclight field corresponds to a solution of Maxwell's equations with aboundary condition defined by the modulated elements of the display 114.

In some implementations, the controller 112 is coupled to theilluminator 116 through a memory buffer. The memory buffer can beconfigured to control amplitude or brightness of light emitting elementsin the illuminator. The memory buffer for the illuminator 116 can have asmaller size than a memory buffer for the display 114. A number of thelight emitting elements in the illuminator 116 can be smaller than anumber of the display elements of the display 114, as long as light fromthe light emitting elements can illuminate over substantially a totalsurface of the display 114. For example, an illuminator having 64×64OLEDs (organic light emitting diodes) can be used for a display having1024×1024 elements. The controller 112 can be configured tosimultaneously activate a number of lighting elements of the illuminator116.

In some implementations, the illuminator 116 is a monochromatic lightsource configured to emit a substantially monochromatic light, e.g., ared light, a green light, a yellow light, or a blue light. In someimplementations, the illuminator 116 includes two or more light emittingelements, e.g., lasers or light emitting diodes (LEDs), each configuredto emit light with a different color. For example, the illuminator 116can include red, green, and blue lighting elements. To display afull-color 3D object, three or more separate holograms for colorsincluding at least red, green, and blue, can be computed. That is, atleast three EM field contributions from corresponding primitives to thedisplay elements can be obtained. The display elements can be modulatedsequentially based on the at least three EM field contributions and theilluminator 116 can be controlled to sequentially turn on the at leastred, green and blue lighting elements sequentially. For example, thecontroller 112 can first transmit a first timing signal to turn on ablue lighting element and transmit first control signals correspondingto a blue hologram to display elements of the display 114. After theblue hologram on the display 114 is illuminated with the blue light fora first period of time, the controller 112 can transmit a second timingsignal to turn on a green lighting element and transmit second controlsignals corresponding to a green hologram to display elements of thedisplay 114. After the green hologram on the display 114 is illuminatedwith the green light for a second period of time, the controller 112 cantransmit a third timing signal to turn on a red lighting element andtransmit third control signals corresponding to a red hologram todisplay elements of the display 114. After the red hologram on thedisplay 114 is illuminated with the red light for a third period oftime, the controller 112 can repeat the above steps. Depending ontemporal coherence-of vision effect in an eye of a viewer, the threecolors can be combined in the eye to give an appearance of full color.In some cases, the illuminator 116 is switched off during a state changeof the display image (or holographic reconstruction) and switched onwhen a valid image (or holographic reconstruction) is presented for aperiod of time. This can also depend on the temporal coherence of visionto make the image (or holographic reconstruction) appear stable.

In some implementations, the display 114 has a resolution small enoughto diffract visible light, e.g., on an order of 0.5 μm or less. Theilluminator 116 can include a single, white light source and the emittedwhite light can be diffracted by the display 114 into different colorsfor holographic reconstructions.

As discussed in further detail below with respect to FIGS. 5A-5K, therecan be different configurations for the system 100. The display 114 canbe reflective or transmissive. The display 114 can have various sizes,ranging from a small scale (e.g., 1-10 cm on a side) to a large scale(e.g., 100-1000 cm on a side). Illumination from the illuminator 116 canbe from the front of the display 114 (e.g., for a reflective ortransflective display) or from the rear of the display 114 (e.g., for atransmissive display). The holographic display device 110 can provideuniform illumination across the display 114. In some implementations, anoptical waveguide, as illustrated in FIGS. 5D-5G, can be used to evenlyilluminate a surface of the display 114. In some examples, thecontroller 112, the illuminator 116, and the display 114 can beintegrated together as a single unit. The integrated single unit caninclude the holographic renderer 130, e.g., in the controller 112.

In some implementations, an optically diffractive device, e.g., a fieldgrating device or a lightguide device as illustrated in FIGS. 5H to 5K,can be configured to diffract light from the illuminator 116 into thedisplay 114, and the display 114 can then diffract the light to aviewer's eyes. In some examples, the light from the illuminator 116 canbe incident on the optically diffractive device with a large incidentangle from a side, such that the illuminator 116 does not block theviewer's view of the display 114. In some examples, the diffracted lightfrom the optically diffractive device can be diffracted at a nearlynormal incident angle into the display, such that the light canrelatively uniformly illuminate the display and be diffracted to theviewer's eyes with reduced (e.g., minimized) loss.

FIG. 1B illustrates a schematic diagram of an example holographicdisplay device 150. The holographic display device 150 can be similar tothe holographic display device 110 of FIG. 1A. The holographic displaydevice 150 includes a computing architecture 152 and a display 156. Thecomputing architecture 152 can be similar to the controller 112 of FIG.1A. The computing architecture 152 can include an array of parallelcomputing cores 154. A computing core can be connected to an adjacentcomputing core via a communication connection 159, e.g., a USB-Cconnection or any other high speed serial (or parallel) connection. Theconnections 159 can be included in a data distribution network throughwhich scene data 151 (e.g., scene primitives) can be distributed amongthe computing cores 154.

The display 156 can be similar to the display 114 of FIG. 1A, and caninclude an array of display elements 160 positioned on a backplane 158.The display elements 160 can be arranged on a front side of thebackplane 158 and the computing cores 154 can be arranged on a back sideof the backplane 158. The backplane 158 can be a substrate, e.g., awafer. The computing cores 154 can be either on the same substrate asthe display 156 or bonded to the back side of the display 156.

Each computing core 154 can be connected to a respective tile (or array)of display elements 160. Each computing core 154 can be configured toperform computations on respective primitives of a number of primitivesin the scene data 151 in parallel with one or more other computingcores. In some examples, the computing core 154 is configured to computean EM field contribution from each of the respective primitives to eachof the array of display elements 160 and generate a sum of EM fieldcontributions from the number of primitives to each of the respectivetiles of display elements 160. The computing core 154 can receive, fromother computing cores of the array of computing cores 154, computed EMfield contributions from other primitives of the number of primitives toeach of the respective tile of display elements 160, and generate thesum of EM field contributions based on the received computed EM fieldcontributions. The computing core 154 can generate a control signal foreach of the respective tile of display elements to modulate at least oneproperty of each of the respective tile of display elements 160 based onthe sum of EM field contributions to the display element.

As noted above, the computing architecture 152 can also generate acontrol signal to an illuminator 162, e.g., in response to determiningthat the computations of the sums of the EM field contributions from thenumber of primitives to each of the display elements have beencompleted. The illuminator 162 emits an input light 153 to illuminatethe modulated display elements 160 and the input light 153 is diffractedby the modulated display elements 160 to form a volumetric light fielde.g., a holographic light field 155, corresponding to the scene data151.

As illustrated in FIG. 1B, the tiles of display elements 160 can beinterconnected into a larger display. Correspondingly, computing cores154 can be interconnected for data communication and distribution. Notethat a parameter that changes in the holographic calculations betweenany given two display elements is their physical locations. Thus, thetask of computing the hologram can be shared between the correspondingcomputing cores 154 equally, and the entire display 150 can operate atthe same speed as a single tile, independent of the number of tiles.

FIG. 1C illustrates an exemplary system 170 for displaying objects in a3D space. The system 170 can include a computing device, e.g., thecomputing device 102 of FIG. 1A, and a holographic display device 172,e.g., the holographic display 110 of FIG. 1A or 150 of FIG. 1B. A usercan use an input device, e.g., a keyboard 174 and/or a mouse 176, tooperate the system 170. For example, the user can create a CG model fora 2D object 178 and a 3D object 180 through the computing device. Thecomputing device or the holographic display device 172 can include aholographic renderer, e.g., the holographic renderer 130 of FIG. 1A, torender the CG model to generate corresponding graphic data for the 2Dobject 178 and the 3D object 180. The graphic data can includerespective primitive data for a list of primitives corresponding to theobjects 178 and 180.

The holographic display device 172 can include a controller, e.g., thecontroller 112 of FIG. 1A or 152 of FIG. 1B, and a display 173, e.g.,the display 114 of FIG. 1A or 156 of FIG. 1B. The controller can computea respective sum of EM field contributions from the primitives to eachdisplay element of the display 173 and generate control signals formodulating each display element based on the respective sum of EM fieldcontributions. The holographic display device 172 can further include anilluminator, e.g., the illuminator 116 of FIG. 1A or the illuminator 162of FIG. 1B. The controller can generate a timing control signal toactivate the illuminator. When light from the illuminator illuminates asurface of the display 173, the modulated display elements can cause thelight to propagate in the 3D space to form a volumetric light fieldcorresponding to a holographic reconstruction for the 2D views of object178 and a holographic reconstruction for the 3D object 180. Thus, the 2Dviews of object 178 and the 3D holographic reconstruction of the object180 are displayed as respective holographic reconstructions floating inthe 3D space in front of, behind, or straddling the display 173.

In some implementations, the computing device transmits non-primitivebased data, e.g., a recorded light field video, to the holographicdisplay device 172. The holographic display device 172 can compute andgenerate corresponding holograms, e.g., a series of sequentialholograms, to display as corresponding holographic reconstructions inthe 3D space. In some implementations, the computing device transmits aCG holographic content simultaneously with live holographic content tothe holographic display device 172. The holographic display device 172can also compute and generate corresponding holograms to display thecontents as corresponding holographic reconstructions in the 3D space.

FIG. 2 illustrates an exemplary configuration 200 for electromagnetic(EM) field calculation. A display 202, e.g., an LCOS device, includingan array of elements 204 and a list of primitives including a pointprimitive 206 are in a 3D space 208. The 3D space 208 includes boundarysurfaces 210. In a 3D coordinate system XYZ, the point primitive 206 hascoordinate information (x, y, z). Each display element 204 lies in aflat plane with respect to other display elements 204 and has a 2Dposition (u, v). The display element 204 also has a location in the 3Dspace. By a mathematical point transformation, the 2D position (u, v)can be transferred into six coordinates 250 in the 3D coordinate system.That is, a surface of the display 202 forms a portion of the boundarysurfaces 210. Thus, EM field contributions from the list of primitivesto a display element computed by defining a boundary condition at thesurface of the display 202 represent a portion of the total EM fieldcontributions from the primitives to the display element. A scalefactor, e.g., six, can be multiplied to a sum of the EM fieldcontributions for each of the display elements to obtain a scaled sum ofthe field contributions, and the display element can be modulated basedon the scaled sum of the field contributions.

Exemplary EM Field Contributions for Primitives

Primitives can be used for computer graphics rendering. Each type ofprimitive in computer graphics corresponds in the formulation of thetechnologies disclosed herein to a discrete mathematical function thatdefines a single holographic primitive for a graphical element added toa hologram. Each type of primitive can correspond to an expression forcalculating an EM field contribution to a display element. A primitivecan be a point primitive, a line primitive, or a polygon (e.g., atriangle) primitive. As illustrated below, an analytic expression can bederived by calculating EM field propagation from a correspondingprimitive to a display element of a display.

FIG. 3A illustrates an example EM propagation from a point primitive 304to an element 302 of a display 300. In a 3D coordinate system XYZ, it isassumed that z coordinate is 0 across the display 300, which meansnegative z values are behind the display 300 and positive z values arein front of the display 300. The point primitive 304 has a coordinate(x, y, z), and the display element 302 has a coordinate (u, v, 0). Adistance d_(u), between the point primitive 304 and the display element302 can be determined based on their coordinates.

The point primitive 304 can be considered as a point charge with timevarying amplitude. According to electromagnetic theory, an electricfield E generated by such a point charge can be expressed as:

$\begin{matrix}{{{E} \propto \frac{\exp\left( {i\; 2\;\pi\; d\text{/}\lambda} \right)}{d^{2}}},} & (1)\end{matrix}$

where λ represents a wavelength of an EM wave, and d represents adistance from the point charge.

Thus, the electric field E_(u,v) at the display element (u,v) can beexpressed as:

$\begin{matrix}{{{E_{u,v}} \propto {\frac{I}{d_{u\; v}^{2}}{\exp\left( {i\; 2\pi\; d_{uv}\text{/}\lambda} \right)}}},} & (2)\end{matrix}$

where I represents a relative intensity of the holographic primitiveelectric field at the display element contributed from the pointprimitive 304.

As discussed above with respect to FIG. 2, a surface of the display 300forms only a portion of a boundary surface for the EM field. A scalefactor S can be applied to the electric field E_(u,v) to get a scaledelectric field E_(φ)(u, v) at the display element that adjusts for thepartial boundary as follows:

$\begin{matrix}{{{E_{\varphi}\left( {u,v} \right)} \propto {\frac{\delta\; I}{d_{uv}^{2}}{\exp\left( {i\; 2\pi\; d_{uv}\text{/}\lambda} \right)}}},} & (3)\end{matrix}$

where δ≅[6+ε],0<ε≤1.

FIG. 3B illustrates an example of EM propagation from a line primitive306 to the display element 302 of the display 300 in the 3D coordinatesystem XYZ. As noted above, the display element 302 can have acoordinate (u, v, 0), where z=0. The line primitive 306 has twoendpoints P₀ with coordinate (x₀, y₀, z₀) and P₁ with coordinate (x₁,y₁, z₁). A distance do between the endpoint P₀ and the display elementcan be determined based on their coordinates. Similarly, a distance d₁between the endpoint P₁ and the display element can be determined basedon their coordinates. A distance d₀₁ between the two endpoints P₀ and P₁can be also determined, e.g., d₀₁=d₁-d₀.

As discussed above, a line primitive can be treated as a superpositionor a linear deformation, and a corresponding analytic expression for theline primitive as a linear aperture can be obtained as a distributeddelta function in space. This analytic expression can be a closedexpression for continuous 3D line segments as holograms.

FIG. 3C illustrates an example EM propagation from a triangle primitive308 to the display element 302 of the display 300 in the 3D coordinatesystem XYZ. As noted above, the display element 302 can have acoordinate (u, v, 0), where z=0. The triangle primitive 308 has threeendpoints: P₀ (x₀, y₀, z₀), P₁ (x₁, y₁, z₁), and P₂ (x₂, y₂, z₂).Distance d₀, d₁, and d₂ between the display element and the endpointsP₀, P₁, and P₂ can be respectively determined based on theircoordinates.

Similar to the line primitive in FIG. 3B, the triangle primitive can betreated as a continuous aperture in space and an analytical expressionfor the EM field contribution of the triangle primitive to the displayelement can be obtained by integration. This can be simplified to obtainan expression for efficient computation.

Exemplary Computations for Primitives

As discussed above, a controller, e.g., the controller 112 of FIG. 1A,can compute an EM field contribution from a primitive to a displayelement based on an analytical expression that can be determined asshown above. As an example, the EM field contribution for a lineprimitive is computed as below.

Each display element in a display has a physical location in space, andeach display element lies in a flat plane with respect to other displayelements. Assuming that the display elements and their controllers arelaid out as is customary in display and memory devices, a simplemathematical point transformation can be used to transform a logicallocation of a given display element based on a logical memory addressfor the display element in a processor to an actual physical location ofthe display element in the space. Therefore, as the logical memoryaddresses of the display elements are looped over in a logical memoryspace of the processor, corresponding actual physical locations in thespace across the surface of the display can be identified.

As an example, if the display has a 5 μm pitch in both x and y, eachlogical address increment can move 5 μm in the x direction, and when anx resolution limit of the display is reached, the next increment willmove back to the initial x physical location and increment the yphysical location by 5 μm. The third spatial coordinate z can be assumedto be zero across the display surface, which means that the negative zvalues are behind the display, and the positive z values are in front ofthe display.

To begin the line calculation, a type of scaled physical distancebetween the current display element and each of the two points of theline primitive can be determined to be d₀ and d₁. As a matter of fact,d₀ and d₁ can be calculated once per primitive, as every subsequentcalculation of the distances across display elements is a smallperturbation of an initial value. In this way, this computation isperformed in one dimension.

An example computation process for each primitive can include thefollowing computation codes:

-   -   DD=f(d1, d0),    -   iscale=SS*COLOR*Alpha1,    -   C1=−2*i scale*sin(DD/2)*sin(Alpha2)*cos(Alpha3),    -   C2=−2*i scale*sin(DD/2)*sin(Alpha2)*sin(Alpha4), where SS,        Alpha1, Alpha2, Alpha3, and Alpha4 are pre-computed constants,        COLOR is the RGB color value passed in with the primitive, and        all values are scalar, single precision floats. Both the sine        and cosine functions can be looked up in tables stored in the        controller to improve computation efficiency.

The results in C1 and C2 are then accumulated for each primitive at eachdisplay element, e.g., in an accumulator for the display element, andcan be normalized once at the end of the computations for the displayelements. At this point, as noted above, the controller can transmit afirst control signal to the display elements to modulate the displayelements based on the computed results and a second control signal to anilluminator to turn on to emit light. Accordingly, a holographicreconstruction (or a holographic light field) is visible to a viewer.When illuminated, the modulated display elements can cause the light toproduce a crisp, continuous color line in three dimensional space.

In some implementations, the computation codes include a hex code forclearing previous accumulations in the accumulator, e.g., at thebeginning of the codes. The computation codes can also include a hexcode for storing the accumulator results into a respective memory bufferfor each display element, e.g., at the end of the codes. In someimplementations, a computing device, e.g., the computing device 102 ofFIG. 1A, transmits a number of background or static primitive hex codesto the controller at an application startup or an interval betweendisplaying frames that does not affect a primary display frame rate. Thecomputing device can then transmit one or more combinations of the hexcodes potentially along with other foreground or dynamic primitives at amuch higher rate to the controller that can form a corresponding controlsignal to modulate the display elements of the display.

The computation process can be orders of magnitude simpler and fasterthan the most efficient line drawing routines in conventional 2D displaytechnology. Moreover, this computation algorithm scales linearly withthe number of display elements. Thus, scaling computing units of thecontroller as a 2D networked processing system can keep up withcomputation needs of an increasing surface area of the display.

Exemplary Computation Implementations

A Maxwell holographic controller, e.g., the controller 112 of FIG. 1A,can compute an EM field contribution from a primitive to a displayelement based on an analytical expression that can be determined asshown above. The controller can be implemented in, for example, an ASIC,an FPGA or GPU, or any combination thereof.

In a modern GPU pipeline, a GPU takes descriptions of geometric figuresas well as vertex and fragment shader programs to produce color anddepth pixel outputs to one or more output image surfaces (called rendertargets). The process involves an explosive fan-out of information wheregeometry is expanded into shading fragments, followed by a visibilitytest to select whether work needs to be done on each of these fragments.A fragment is a record that contains all the information involved toshade that sample point, e.g., barycentric coordinates on the triangle,interpolated values like colors or texture coordinates, surfacederivatives, etc. The process of creating these records then rejectingthose that do not contribute to the final image is the visibility test.Fragments that pass the visibility test can be packed into work groupscalled wavefronts or warps that are executed in parallel by the shaderengines. These produce output values that are written back to memory aspixel values, ready for display, or for use as input textures for laterrendering passes.

In Maxwell holography, the rendering process can be greatly simplified.In Maxwell holographic calculations, every primitive can contribute toevery display element. There is no need to expand geometry into pixelsand no need to apply visibility tests before packing wavefronts. Thiscan also remove the need for decision making or communication betweenMaxwell holographic pipelines and allow computation to become a parallelissue with a number of possible solutions each one tuned to speed, cost,size or energy optimization. The graphics pipeline is significantlyshorter with fewer intermediate steps, no data copying or movement, andfewer decisions leading to lower latency between initiating a draw andthe result being ready for display. This can allow Maxwell holographicrendering to create extremely low latency displays. As discussed below,this can allow Maxwell holographic calculations to increase accuracy,for example, by using fixed point numbers in the Maxwell holographicpipeline, and to optimize computation speed, for example, by optimizingmathematical functions.

Using Fixed Point Numbers

When calculating an EM contribution from each primitive at each displayelement (or “phasel”), intermediate calculations involve producing verylarge numbers. These large numbers involve special handling as they alsoneed to retain the fractional parts during the calculation.

Floating point values have the disadvantage that they are most accurateclose to the origin (zero on the number line) and lose one bit ofaccuracy every power-of-two when moving away from the origin. Fornumbers close in the range [−1,1], the accuracy of floating point valuescan be exquisite, but once reaching numbers in the tens of millions,e.g., reaching the point where single-precision 32-bit IEEE-754 floatingpoint values have no fractional digits remaining, the entire significand(a.k.a mantissa) is used to represent the integer part of the value.However, it is the fractional part of large numbers that Maxwellholography is particularly interested in retaining.

In some cases, fixed point numbers are used in the Maxwell holographiccalculations. Fixed point number representations are numbers where thedecimal point does not change on a case-by-case basis. By choosing thecorrect numbers of bits for the integer and fractional parts of anumber, the same number of fractional bits can be obtained regardless ofthe magnitude of the number. Fixed point numbers are represented asintegers with an implicit scale factor, e.g., 14.375 can be representedas the number 3680 (0000111001100000 base-2) in a 16-bit fixed pointvalue with 8 fractional bits. This can be also represented as an“unsigned 16.8” fixed point number, or u16.8 for short. Negative numberscan have one additional sign bit and are stored in “2s compliment”format. In such a way, the accuracy of the calculation can be greatlyimproved.

Optimization to Mathematical Functions

As shown above, Maxwell holographic calculations involve the use oftranscendental mathematical functions, e.g., sine, cosine, arc tangent,etc. In a CPU, these functions are implemented as floating point libraryfunctions that can use specialized CPU instructions, or on a GPU asfloating point units in the GPU. These functions are written to takearguments as a floating point number and the results are returned in thesame floating point representation. These functions are built for thegeneral case, to be accurate where floats are accurate, to be correctlyrounded and to cope with every edge case in the floating point numberrepresentation (+/−Infinity, NaN, signed zero, and denormal floats).

In Maxwell holographic calculations, with the fixed pointrepresentation, there is no need to use denormal floats for gradualunderflow, no need to handle NaN results from operations like divisionby zero, no need to alter the floating point rounding modes, and no needto raise floating point exceptions to the operating system. All of theseallow simplifying (and/or optimizing) the transcendental mathematicalfunctions, for example, as discussed below.

In some cases, optimizations can be made to take arguments in one fixedpoint format and return the value to a different level of accuracy,e.g., input s28.12 and output s15.14. This can be especially desirablewhen calculating the sine of large values in the 10s of millions, theinput argument can be large but the output can only need to representthe value range [−1, 1], or arctangent which takes in any value butreturn values in the range [−π/2, π/2].

In some cases, optimization can be made to freely implement thetranscendental functions as fully enumerated look-up tables, asinterpolated tables, as semi-table based polynomial functions, or assemi-table based full minimax polynomials, depending on the input rangeinvolved. It also allows to apply specialized range reduction methodsthat cope with large inputs, which the general purpose GPU pipelinecalculation can skip for speed.

In some cases, another optimization can be transforming trigonometriccalculations from the range [−π, π] into a signed 2's complimentrepresentation in the range [−1,1] which has the advantage of notrequiring expensive modulo a division operations.

Exemplary Implementations for Occlusion

Occlusion is often viewed as a difficult and important topic in computergraphics, and even more so in computational holography. This is because,in at least some cases, while the occlusion problem in projective CGI isstatic, what is hidden and what is visible in holographic systems dependon the location, orientation, and direction of a viewer. Wave approachesof G-S holography or its derivatives have been developed to address theholographic occlusions. However, masking or blocking contributions fromparts of a scene that are behind other parts of a scene can be verycomplicated and computationally expensive in the G-S methodology.

In Maxwell holography, the occlusion issue can be addressedcomparatively easily, because which display elements (e.g., phasels)correspond to which primitives is completely deterministic and trivial.For example, whether or not a given display element contributes to areconstruction of a given primitive can be determined as the calculationfor the given primitive is performed. After determining that a number ofdisplay elements do not contribute to the given primitive due toocclusion, when calculating a sum of EM contributions to one of thenumber of display elements, the EM contribution from the given primitiveis omitted from the calculation of the sum of EM contributions to theone of the number of display elements.

For illustration only, FIGS. 3D-3F show a determination of displayelements not contributing to a given primitive (a point in FIG. 3D, aline in FIG. 3E, and a triangle in FIG. 3F) with a line primitive as anoccluder. The line primitive has a starting point O1 and an ending pointO2.

As illustrated in FIG. 3D, a point primitive P0 is behind the occluderand closer to the display. By extending lines connecting O1-P0 andO2-P0, a range of display elements from D1 to D2 in the display isdetermined, which do not contribute to the reconstruction of the pointprimitive P0.

In some examples, the coordinate information of O1, O2, and P0 is known,e.g., stored in a “Z” buffer calculated by a GPU (e.g., the GPU 108 ofFIG. 1A) prior to the scene being transmitted to the Maxwell holographiccontroller (e.g., the controller 112 of FIG. 1A). For example, in an XZplane with y=0, the coordinate information can be O1 (Ox1, Oz1), O2(Ox2, Oz2), and P0 (Px, Pz), with Oz1=Oz2=Oz. Based on the coordinateinformation, the coordinate information of D1 and D2 can be determinedto be

Dx1=Px+ρ(Px−Ox2), Dx2=Dx1+ρ(Ox2−Ox1)  (4),

where ρ=Pz/(Oz−Pz), and Dz1=Dz2=0.

The information of D1 and D2 can be stored as additional information inan “S” buffer for the Maxwell holographic controller, besides theinformation in a Z buffer for the point primitive P₀. In such a way, theadditional information can be used to trivially mask the contributionsof specific display elements (within the range from D1 to D2) to thespecific primitive P0 in the indexed primitive list.

FIG. 3E illustrates a determination of how a specific display elementcontributes to a line primitive with an occluder before (or in front of)the line primitive. By connecting the specific display element D0 to thestarting point O₁ and the ending point O₂ of the occluder, two pointprimitives P1 and P2 on the line primitive are determined as theintersection points. Thus, the specific display element D0 does notcontribute to the reconstruction of the part of the line primitive fromP1 to P2 on the line primitive. Accordingly, when calculating the sum ofEM contributions to the specific display element D0, the EMcontributions from the part P1-P2 of the line primitive is notcalculated.

This can be implemented in two ways. In the first way, the EMcontributions from the part P0-P1 and the part P2-Pn to the specificdisplay element D0 are summed as the EM contributions of the lineprimitive to the specific display element D0, by considering theocclusion from the occluder. In the second way, the EM contribution fromthe whole line primitive P0-Pn is calculated, together with the EMcontribution from the part P1-P2, and a difference between the twocalculated EM contributions can be considered as the EM contribution ofthe line primitive to the specific display element D0 by considering theocclusion from the occluder. The coordinate information of P1 and P2 orthe part P1-P2 can be stored, as the part of the line primitive thatdoes not contribute to the specific display element D0, in the “S”buffer of the Maxwell holographic controller, together with theinformation of the occluder and other information in the “Z” buffer ofthe GPU.

FIG. 3F illustrates a determination of how a specific display elementcontributes to a triangle primitive with an occluder before the triangleprimitive. By connecting the specific display element D0 to the startingpoint O1 and the ending point O2 of the occluder, four point primitivesP1, P2, P3, and P4 on sides of the triangle primitive are determined asthe intersection points. Thus, the specific display element D0 does notcontribute to the reconstruction of the part of the triangle primitiveenclosed by the points P1, P2, P3, P4, P_(C). Accordingly, whencalculating the sum of EM contributions to the specific display elementD0, the EM contributions from the part P1-P2-P3-P4-P_(C) of the triangleprimitive is not calculated. That is, only the EM contributions from thefirst triangle formed by points P_(A), P1 and P2 and the second triangleformed by points P_(B), P3, and P4 are summed as the EM contribution ofthe triangle primitive P_(A)-P_(B)-P_(C) by considering the occlusion ofthe occluder. The coordinate information of P1, P2, P3, and P4 or thetriangle primitives P_(A)-P1-P2 and P_(B)-P3-P4 can be stored, as thepart of triangle primitive P_(A)-P_(B)-P_(C) that contributes to thespecific display element D0, in the “S” buffer of the Maxwellholographic controller, together with the information of the occluderand other information in the “Z” buffer of the GPU.

The implementations of occlusion in Maxwell holography enables toconvert the “Z” buffer in the GPU to the “S” buffer in the Maxwellholographic controller, and can mask the contributions of specificprimitives (or specific parts of the primitives) in the indexedprimitive list to a specific display element. This not only providesaccurate, physically correct occlusion, it also saves computation time,as the primitives that do not contribute to a given display element canbe ignored and computation can move on to computation for the nextdisplay element. The “S” buffer can contain additional informationrelated to diffraction efficiency of the display.

The “S” buffer can also include rendering features such as Holographicspecular highlights, in which a reflectivity of a surface is dependentupon the viewing angle. In traditional CGI, specular highlights aredependent only on the orientation of the rendered object, whereas in aMaxwell holographic context, the direction from which the object isviewed also plays a part. Therefore, the geometric specular informationcan be encoded in the “S” buffer as an additive (specular) rather than asubtractive (occlusion) contribution. In Maxwell holography, themathematics for holographic specular highlights can be substantially thesame as that for holographic occlusion.

Exemplary Implementations for Stitching

When light illuminates a display modulated with EM contributions from alist of primitives of a 3D object, the modulated display causes thelight to propagate in different directions to form a volumetric lightfield corresponding to the primitives. The volume light field is theMaxwell holographic reconstruction. Two adjacent primitives in the 3Dobject, e.g., two triangle primitives, have a shared side (e.g., edge orsurface). During the reconstruction, a stitching issue may raise, wherethe light intensity of the shared side can be doubled due to thereconstructions of the two adjacent primitives separately. This mayaffect the appearance of the reconstructed 3D object.

To address the stitching issue in Maxwell holography, as illustrated inFIG. 3G, the adjacent primitives can be scaled down by a predeterminedfactor, so that a gap can be formed between the adjacent primitives. Insome cases, instead of scaling down the two adjacent primitives, onlyone primitive or a part of the primitive is scaled down. For example, aline of a triangle primitive can be scaled down to separate from anothertriangle primitive. In some cases, the scaling can include scalingdifferent parts of a primitive with different predetermined factors. Thescaling can be designed such that the gap is big enough to separate theadjacent primitives to minimize the stitching issue and small enough tomake the reconstructed 3D object appear seamless. The predeterminedfactor can be determined based on information of the display and of theviewer, e.g., a maximum spatial resolution of the holographic lightfield and, in the case of a part of a primitive appearing entirely orpartially behind the display, a minimum distance from the viewer to thatpart of the primitive.

In some cases, the scaling operation can be applied to primitive data ofa primitive obtained from the holographic renderer, e.g., theholographic renderer 130 of FIG. 1A, and the scaled primitive data ofthe primitive is sent to the Maxwell holographic controller, e.g., thecontroller 112 of FIG. 1A. In some cases, the controller can perform thescaling operation on the primitive data obtained from the holographicrenderer, before calculating EM contributions of the primitives to thedisplay elements of the display.

Exemplary Implementations for Texture Mapping

Texture mapping is a technique developed in computer graphics. The basicidea is to take a source image and apply it as a decal to a surface in aCGI system, enabling detail to be rendered into the scene without theneed for the addition of complex geometry. The texture mapping caninclude techniques for the creation of realistic lighting and surfaceeffects in the CGI system, and can refer universally to the applicationof surface data to triangular meshes.

In Maxwell holography, flat shaded and also interpolated triangularmeshes can be rendered in genuine 3D using the analytic relationshipbetween arbitrary triangles in space and a phase map on a holographicdevice. However, to be compatible with modern rendering engines, theability to map information on the surface of these triangles isdesirable. This can present a real problem, in that the speed of themethod is derived from the existence of the analytic mapping, which doesnot admit data-driven amplitude changes.

Discrete Cosine Transform (DCT) is an image compression technique andcan be considered as the real-valued version of the FFT (Fast Fouriertransform). DCT depends on an encode-decode process that assigns weightsto cosine harmonics in a given image. The result of an encode is a setof weights equal in number to the number of pixels in the originalimage, and if every weight is used to reconstruct an image, there willbe no loss in information. However, in many images, acceptablereconstructions can be made from a small subset of the weights, enablinglarge compression ratios.

The decode (render) process of the DCT in two dimensions involves aweighted double sum over every DCT weight and every destination pixel.This can be applied to Maxwell holography for texture mapping. InMaxwell holography, triangle rendering involves a “spiked” doubleintegral, in phase space, to determine the phase contribution of anyindividual phasel to the triangle in question. The integral can befolded into a double sum which mirrors the one in the DCTreconstruction, and then re-derive the analytic triangle expression interms of the DCT weights. This implementation of DCT technique inMaxwell holographic calculations enables to draw full, texture mappedtriangles, to employ image compression to the data for the renderedtexture triangles, and to take advantage of existing toolsets thatautomatically compress texture and image data using DCT such as JPEG.

In some implementations, to draw a Maxwell holographic texturedtriangle, a spatial resolution desired for the mapping on a specifiedsurface is first calculated. Then a texture with the resolution issupplied, and DCT compressed with angular and origin information tocorrectly orient it on the triangle is obtained. Then, the trianglecorners and a list of DCT weights are included in the indexed primitivelist and sent to the Maxwell holographic controller. The DCT weights canbe included in the EM contributions of the triangle primitive to eachdisplay element. The texture triangle can be n times slower than a flattriangle, where n is the number of (nonzero) DCT weights that are sentwith the primitive. Modern techniques for “fragment shading” can beimplemented in the Maxwell holographic system, with the step of the DCTencode replacing the filter step for traditional projective rendering.

As an example, the following expression shows the DCT weights B_(pq) foran image:

$\begin{matrix}{{{B_{pq} \equiv {\sigma_{p}\sigma_{q}{\sum\limits_{m = 0}^{M - 1}\;{\sum\limits_{n = 0}^{N - 1}\;{A_{mn}{\cos\;\left\lbrack \frac{{\pi\left( {{2m} + 1} \right)}p}{2M} \right\rbrack}{\cos\;\left\lbrack \frac{{\pi\left( {{2n} + 1} \right)}q}{2N} \right\rbrack}}}}}},{where}}{\sigma_{p} = \left\{ {\begin{matrix}{1\text{/}\sqrt{M}} & {p = 0} \\\sqrt{2\text{/}M} & {else}\end{matrix},{\sigma_{q} = \left\{ {\begin{matrix}{1\text{/}\sqrt{N}} & {q = 0} \\\sqrt{2\text{/}N} & {else}\end{matrix},} \right.}} \right.}} & (5)\end{matrix}$

M and N are corners of a rectangular image, and (p, q) is a DCT term.

By decoding, the amplitude value A_(mn) can be obtained as follows:

$\begin{matrix}{{{A_{mn} = {\sum\limits_{p = 0}^{M - 1}\;{\sum\limits_{q = 0}^{N - 1}{\sigma_{p}\sigma_{q}A_{mn}^{*}}}}},{where}}{A_{mn}^{*} = {B_{pq}{\cos\;\left\lbrack \frac{{\pi\left( {{2m} + 1} \right)}p}{2M} \right\rbrack}{{\cos\;\left\lbrack \frac{{\pi\left( {{2n} + 1} \right)}q}{2N} \right\rbrack}.}}}} & (6)\end{matrix}$

When calculating the EM contribution of the textured triangle primitiveto a display element (e.g., a phasel), a DCT term with a correspondingDCT weight A*_(mn) can be included in the calculation as follows:

φ_(pq)=Σ_(y=0) ^(Y)Σ_(x=0) ^(X) A* _(mn) T  (7),

where λ Y are corners of the triangle in the coordinate system, Tcorresponds to the EM contribution of the triangle primitive to thedisplay element, and φ_(pq) is the partial contribution for non-zeroterm B_(pq) in the DCT. The number of (p,q) DCT terms can be selected byconsidering both the information loss in reconstruction and theinformation compression.

Exemplary Process

FIG. 4 is a flowchart of an exemplary process 400 of displaying anobject in 3D. The process 400 can be performed by a controller for adisplay. The controller can be the controller 112 of FIG. 1A or 152 ofFIG. 1B. The display can the display 114 of FIG. 1A or 156 of FIG. 1B.

Data including respective primitive data for primitives corresponding toan object in a 3D space is obtained (402). The data can be obtained froma computing device, e.g., the computing device 102 of FIG. 1A. Thecomputing device can process a scene to generate the primitivescorresponding to the object. The computing device can include a rendererto generate the primitive data for the primitives. In someimplementations, the controller generates the data itself, e.g., byrendering the scene.

The primitives can include at least one of a point primitive, a lineprimitive, or a polygon primitive. The list of primitives is indexed ina particular order, e.g., by which the object can be reconstructed. Theprimitive data can include color information that has at least one of atextured color, a gradient color, or a constant color. For example, theline primitive can have at least one of a gradient color or a texturedcolor, or a constant color. The polygon primitive can also have at leastone of a gradient color, a textured color, or a constant color. Theprimitive data can also include texture information of the primitiveand/or shading information on one or more surfaces of the primitive(e.g., a triangle). The shading information can include a modulation onat least one of color or brightness on the one or more surfaces of theprimitive. The primitive data can also include respective coordinateinformation of the primitive in the 3D coordinate system.

The display can include a number of display elements, and the controllercan include a number of computing units. Respective coordinateinformation of each of the display elements in the 3D coordinate systemcan be determined based on the respective coordinate information of thelist of primitives in the 3D coordinate system. For example, a distancebetween the display and the object corresponding to the primitives canbe predetermined. Based on the predetermined distance and the coordinateinformation of the primitives, the coordinate information of the displayelements can be determined. The respective coordinate information ofeach of the display elements can correspond to a logical memory addressfor the element stored in a memory. In such a way, when the controllerloops in a logical memory address for a display element in a logicalmemory space of the controller, a corresponding actual physical locationfor the display element in the space can be identified.

An EM field contribution from each of the primitives to each of thedisplay elements is determined by calculating EM field propagation fromthe primitive to the element in the 3D coordinate system (404). The EMfield contribution can include at least one of a phase contribution oran amplitude contribution.

As illustrated above with respect to FIGS. 3A-3C, at least one distancebetween the primitive and the display element can be determined based onthe respective coordinate information of the display element and therespective coordinate information of the primitive. In some cases, foreach primitive, the at least one distance can be calculated or computedjust once. For example, the controller can determine a first distancebetween a first primitive of the primitives and a first element of thedisplay elements based on the respective coordinate information of thefirst primitive and the respective coordinate information of the firstelement and determining a second distance between the first primitiveand a second element of the elements based on the first distance and adistance between the first element and the second element. The distancebetween the first element and the second element can be predeterminedbased on a pitch of the plurality of elements of the display.

The controller can determine the EM field contribution to the displayelement from the primitive based on a predetermined expression for theprimitive and the at least one distance. In some cases, as illustratedabove with respect to FIGS. 3A-3C, the predetermined expression can bedetermined by analytically calculating the EM field propagation from theprimitive to the element. In some cases, the predetermined expression isdetermined by solving Maxwell's equations. Particularly, the Maxwell'sequations can be solved by providing a boundary condition defined at asurface of the display. The boundary condition can include a Dirichletboundary condition or a Cauchy boundary condition. The primitives andthe display elements are in the 3D space, and the surface of the displayforms a portion of a boundary surface of the 3D space. The predeterminedexpression can include at least one of functions that include a sinefunction, a cosine function, and an exponential function. Duringcomputation, the controller can identify a value of the at least one ofthe functions in a table stored in a memory, which can improve acomputation speed. The controller can determine the EM fieldcontribution to each of the display elements for each of the primitivesby determining a first EM field contribution from a first primitive to adisplay element in parallel with determining a second EM fieldcontribution from a second primitive to the display element.

For each of the display elements, a sum of the EM field contributionsfrom the list of primitives to the display element is generated (406).

In some implementations, the controller determines first EM fieldcontributions from the primitives to a first display element and sumsthe first EM field contributions for the first element and determiningsecond EM field contributions from the primitives to a second displayelement and sums the second EM field contributions for the seconddisplay element. The controller can include a number of computing units.The controller can determine an EM field contribution from a firstprimitive to the first element by a first computing unit in parallelwith determining an EM field contribution from a second primitive to thefirst element by a second computing unit.

In some implementations, the controller determines first respective EMfield contributions from a first primitive to each of the displayelements and determine second respective EM field contributions from asecond primitive to each of the display elements. Then the controlleraccumulates the EM field contributions for the display element by addingthe second respective EM field contribution to the first respective EMfield contribution for the display element. Particularly, the controllercan determine the first respective EM field contributions from the firstprimitive to each of the display elements by using a first computingunit in parallel with determining the second respective EM fieldcontributions from the second primitive to each of the display elementsby using a second computing unit.

A first control signal is transmitted to the display, the first controlsignal being for modulating at least one property of each displayelement based on the sum of the field distributions to the displayelement (408). The at least one property of the element includes atleast one of a refractive index, an amplitude index, a birefringence, ora retardance.

The controller can generate, for each of the display elements, arespective control signal based on the sum of the EM field contributionsfrom the primitives to the element. The respective control signal is formodulating the at least one property of the element based on the sum ofthe EM field contributions from the primitives to the element. That is,the first control signal includes the respective control signals for thedisplay elements.

In some examples, the display is controlled by electrical signals. Thenthe respective control signal can be an electrical signal. For example,an LCOS display includes an array of tiny electrodes whose voltage isindividually controlled as element intensities. The LCOS display can befilled with a birefringent liquid crystal (LC) formulation that changesits refractive index as an applied voltage changes. Thus, the respectivecontrol signals from the controller can control the relative refractiveindex across the display elements and accordingly the relative phase oflight passing through or reflected by the display.

As discussed above, the display surface forms a part of the boundarysurface. The controller can multiple a scale factor to the sum of thefield contributions for each of the elements to obtain a scaled sum ofthe field contributions, and generate the respective control signalbased on the scaled sum of the field contributions for the element. Insome cases, the controller can normalize the sum of the fieldcontributions for each of the elements, e.g., among all the elements,and generate the respective control signal based on the normalized sumof the field contributions for the element.

A second control signal is transmitted to an illuminator as a controlsignal for turning on the illuminator to illuminate light on themodulated display (410). The controller can generate and transmit thesecond control signal in response to determining a completion ofobtaining the sum of the field contributions for each of the displayelements. Due to time symmetry (or conservation of energy), themodulated elements of the display can cause the light to propagate indifferent directions to form a volumetric light field corresponding tothe object in the 3D space. The volumetric light field can correspond toa solution of Maxwell's equations with a boundary condition defined bythe modulated elements of the display.

In some implementations, the illuminator is coupled to the controllerthrough a memory buffer configured to control amplitude or brightness ofone or more light emitting elements in the illuminator. The memorybuffer for the illuminator can have a smaller size than a memory bufferfor the display. A number of the light emitting elements in theilluminator can be smaller than a number of the elements of the display.The controller can be configured to activate the one or more lightemitting elements of the illuminator simultaneously.

In some examples, the illuminator includes two or more light emittingelements each configured to emit light with a different color. Thecontroller can be configured to sequentially modulate the display withinformation associated with a first color during a first time period andmodulate the display with information associated with a second colorduring a second, sequential time period, and to control the illuminatorto sequentially turn on a first light emitting element to emit lightwith the first color during the first time period and a second lightemitting element to emit light with the second color during the secondtime period. In such a way, a multi-color object can be displayed in the3D space.

In some examples, the display has a resolution small enough to diffractlight. The illuminator can emit a white light into the display which candiffract the white light into light with different colors to therebydisplay a multi-color object.

Exemplary Systems

FIGS. 5A-5K show implementations of example systems for 3D displays. Anyone of the systems can correspond to, for example, the system 100 ofFIG. 1A. FIGS. 5A and 5B show example systems having reflective displayswith front illumination. FIG. 5C shows an example system having atransmissive display with back illumination. FIGS. 5D and 5E showexample systems having transmissive displays with waveguideillumination. FIGS. 5F and 5G show example systems having reflectivedisplays with waveguide illumination. FIGS. 5H and 5I show examplesystems having reflective displays with optically diffractiveillumination using a transmissive grating structure (FIG. 5H) and areflective grating structure (FIG. 5I). FIGS. 5J and 5K show examplesystems having transmissive displays with optically diffractiveillumination using a reflective grating structure (FIG. 5J) and atransmissive grating structure (FIG. 5K).

FIG. 5A illustrates a system 500 with a reflective display with frontillumination. The system 500 includes a computer 502, a controller 510(e.g., an ASIC), a display 512 (e.g., an LCOS device), and anilluminator 514. The computer 502 can be the computing device 102 ofFIG. 1A, the controller 510 can be the controller 112 of FIG. 1A, thedisplay 512 can be the display 114 of FIG. 1A, and the illuminator 514can be the illuminator 116 of FIG. 1A.

As illustrated in FIG. 5A, the computer 502 includes an application 504that has a renderer 503 for rendering a scene of an object. The renderedscene data is processed by a video driver 505 and then a GPU 506. TheGPU 506 can be the GPU 108 of FIG. 1A and can be configured to generatea list of primitives corresponding to the scene and respective primitivedata. For example, the video driver 505 can be configured to process therendered scene data and generate a list of primitives. As noted above,the GPU 506 can include a conventional 2D renderer, e.g., theconventional 2D renderer 120 of FIG. 1A, to render the primitives into alist of items to draw on a 2D display 508. The GPU 506 or the controller510 can include a holographic renderer, e.g., the holographic renderer130 of FIG. 1A, to render the list of primitives into graphic data to bedisplayed by the display 512.

The controller 510 is configured to receive the graphic data from thecomputer 502, compute EM field contributions from the list of primitivesto each of elements of the display 512, and generate a respective sum ofthe EM field contributions from the primitives to each of the elements.The controller 510 can generate respective control signals to each ofthe display elements for modulating at least one property of the displayelement. The controller can transmit the respective control signals tothe display elements of the display 512 through a memory buffer 511 forthe display 512.

The controller 510 can also generate and transmit a control signal,e.g., an illumination timing signal, to activate the illuminator 514.For example, the controller 510 can generate and transmit the controlsignal in response to determining that the computations of the sums ofEM field contributions from the primitives to the display elements arecompleted. As noted above, the controller 510 can transmit the controlsignal to the illuminator 514 via a memory buffer. The memory buffer canbe configured to control amplitude or brightness of light emittingelements in the illuminator 514 and activate the light emitting elementssimultaneously or sequentially.

As illustrated in FIG. 5A, the illuminator 514 can emit a collimatedlight beam 516 that is incident on a front surface of the display 512 atan incident angle in a range between 0 degrees and almost ±90 degrees.The emitted light beam is diffracted from the display 512 to form aholographic light field 518, corresponding to the object, which can beseen by a viewer.

FIG. 5B illustrates another system 520 with another reflective display524 with front illumination. Compared to the system 500 of FIG. 5A, thesystem 520 has a larger reflective display 524. To accommodate this, orfor other packaging or aesthetic reasons, a display controller 522 isincluded in a housing that can be a support or enclosure for anilluminator 526. The controller 522 is similar to the controller 510 ofFIG. 5A and can be configured to receive graphic data from a computer521, compute EM field contributions from primitives to each of displayelements of the display 524, and generate a respective sum of the EMfield contributions from the primitives to each of the display elements.The controller 522 then generates respective control signals to each ofthe display elements for modulating at least one property of the displayelement and transmits the respective control signals to the displayelements of the display 524 through a memory buffer 523 for the display524.

The controller 522 also transmits a control signal to the illuminator526 to activate the illuminator 526. The illuminator 526 emits adivergent or semi-collimated light beam 527 to cover a whole surface ofthe display 524. The light beam 524 is diffracted by the modulateddisplay 524 to form a holographic light field 528.

FIG. 5C illustrates a system 530 with a transmissive display 534 withback illumination. The transmissive display 534, for example, can be alarge scale display. The system 530 includes a controller 532 which canbe similar to the controller 510 of FIG. 5A. The controller 532 can beconfigured to receive graphic data from a computer 531, compute EM fieldcontributions from primitives to each of display elements of the display534, and generate a respective sum of the EM field contributions fromthe primitives to each of the display elements. The controller 532 thengenerates respective control signals to each of the display elements formodulating at least one property of the display element and transmitsthe respective control signals to the display elements of the display534 through a memory buffer 533 for the display 534.

The controller 532 also transmits a control signal to an illuminator 536to activate the illuminator 536. Different from the system 500 of FIG.5A and the system 520 of FIG. 5B, the illuminator 536 in the system 530is positioned behind a rear surface of the display 534. To cover a largesurface of the display 534, the illuminator 536 emits a divergent orsemi-collimated light beam 535 on to the rear surface of the display534. The light beam 535 is transmitted through and diffracted by themodulated display 534 to form a holographic light field 538.

FIG. 5D illustrates another system 540 with a transmissive display 544with waveguide illumination. The system 540 also includes a controller542 and an illuminator 546. The controller 542 can be similar to thecontroller 510 of FIG. 5A, and can be configured to receive graphic datafrom a computer 541, perform computation on the graphic data, generateand transmit control signals for modulation to the display 544 and atiming signal to activate the illuminator 546.

The illuminator 546 can include a light source 545 and include or beoptically attached to a waveguide 547. Light emitted from the lightsource 545 can be coupled to the waveguide 547, e.g., from a sidecross-section of the waveguide. The waveguide 547 is configured to guidethe light to illuminate a surface of the display 544 uniformly. Thelight guided by the waveguide 547 is incident on a rear surface of thedisplay 544 and transmitted through and diffracted by the display 544 toform a holographic light field 548.

Different from the system 500 of FIG. 5A, 520 of FIG. 5B, 530 of FIG.5C, in the system 540, the controller 542, the display 544, and thewaveguide 547 are integrated together into a single unit 550. In somecases, the waveguide 547 and the light source 545 can be integrated asan active waveguide illuminator in a planar form, which can furtherincrease a degree of integration of the single unit 550. As discussedabove, the single unit 500 can be connected or tiled with other similarunits 550 to form a larger holographic display device.

FIG. 5E illustrates another system 560 with another transmissive display564 with waveguide illumination. Compared to the system 540, thetransmissive display 564 can potentially implement a display that islarger than the transmissive display 544. For example, the transmissivedisplay 564 can have a larger area than a controller 562, and toaccommodate this, the controller 562 can be positioned away from thedisplay 564. The system 560 includes an illuminator 566 that has a lightsource 565 and a waveguide 567. The waveguide 567 is integrated with thedisplay 564, e.g., optically attached, to a rear surface of the display564. In some implementations, the display 564 is fabricated on a frontside of a substrate and the waveguide 567 can be fabricated on a backside of the substrate.

The controller 562 can be similar to the controller 510 of FIG. 1A andconfigured to receive graphic data from a computer 561, performcomputation on the graphic data, generate and transmit control signalsfor modulation to the display 564 through a memory buffer 563 and atiming signal to activate the light source 565. Light emitted from thelight source 565 is guided in the waveguide 567 to illuminate the rearsurface of the display 564 and transmitted and diffracted through thedisplay 564 to form a holographic light field 568.

FIG. 5F illustrates another system 570 with a reflective display 574with waveguide illumination. The reflective display 574, for example,can be a large display. A waveguide 577 of an illuminator 576 ispositioned on a front surface of the reflective display 574. Acontroller 572, similar to the controller 510 of FIG. 5A, can beconfigured to receive graphic data from a computer 571, performcomputation on the graphic data, generate and transmit control signalsfor modulation to the display 574 through a memory buffer 573 and atiming signal to activate a light source 575 of the illuminator 576.Light coupled from a waveguide 577 of the illuminator 576 is guided tobe incident on the front surface of the display 574 and diffracted bythe display 574 to form a holographic light field 578.

FIG. 5G illustrates another system 580 with a reflective display 584with another type of waveguide illumination using a waveguide device588. A controller 582, similar to the controller 510 of FIG. 5A, isconfigured to generate and transmit controls signals corresponding toholographic data (images and/or videos) for modulation of the display584 and transmit a timing signal to activate an illuminator 586. Theilluminator 586 can provide one or more colors of light that can becollimated. The waveguide device 588 is positioned in front of theilluminator 586 and the display 584. The waveguide device 588 caninclude an input coupler 588-1, a waveguide 588-2, and an output coupler588-3. The input coupler 588-1 is configured to couple the collimatedlight from the illuminator 586 into the waveguide 588-2. The light thentravels inside the waveguide 588-2 via total internal reflection and isincident at the end of the waveguide 588-2 on the output coupler 588-3.The output coupler 588-3 is configured to couple out the light into thedisplay 584. The light then illuminates the display elements of thedisplay 584 that are modulated with corresponding control signals and isdiffracted by the reflective display 584 and reflected back (e.g., by aback mirror of the display 584) through the waveguide device 588 (e.g.,the output coupler 588-3) to form a holographic light fieldcorresponding to the holographic data in front of a viewer.

In some examples, light is coupled out by the output coupler 588-3 at anangle normal to the waveguide device 588 and/or a front surface of thereflective display 584. In some examples, each of the input coupler588-1 and the output coupler 588-2 can include a grating structure,e.g., a Bragg grating. The input coupler 588-1 and the output coupler588-2 can include a similar diffraction grating with different fringetilt angle. In some examples, the illuminator 586 provides a singlecolor of light, and the input coupler 588-1 and the output coupler 588-2includes a diffraction grating for the color. In some examples, theilluminator 586 provides multiple colors of light, e.g., red, green andblue light beams, and the input coupler 588-1 and the output coupler588-2 can include a multilayer stack of three corresponding diffractiongratings (or a single layer having the three corresponding diffractiongratings) that respectively couple in or couple out the different colorlight beams.

FIG. 5H illustrates another system 590 with a reflective display 594with optically diffractive illumination using an optically diffractivedevice 598. The optically diffractive device 598 can be considered as alightguide device for guiding light. The optically diffractive device598 can be a transmissive field grating based structure that can includeone or more transmissive holographic gratings. The reflective display594 can be a reflective LCOS device. A controller 592, similar to thecontroller 510 of FIG. 5A, can be configured to receive graphic datacorresponding to one or more objects from a computer 591, performcomputation on the graphic data, and generate and transmit controlsignals for modulation to the display 594 through a memory buffer 593.The controller 592 can be also coupled to an illuminator 596 and beconfigured to provide a timing signal to activate the illuminator 596 toprovide light. The light is then diffracted by the optically diffractivedevice 598 to be incident on the display 594 and then diffracted by thedisplay 594 to form a holographic light field 599 corresponding to theone or more objects. The display 594 can include a back mirror on theback of the display 594 and can reflect the light towards the viewer.The optically diffractive device 598 can be optically transparent. Theilluminator 596 can be positioned below the display 594, which can allowthe illuminator 596 to be mounted or housed with other components of thesystem 590 and to be below an eyeline of the viewer.

As discussed with further details below, Bragg selectivity allowsoff-axis illumination light to be diffracted from the opticallydiffractive device 598 towards the display 594 while the returning lightdiffracted from the display 594 can be close to on axis and hence beoff-Bragg to the gratings in the optically diffractive device 598 andhence can pass through the optically diffractive device 598 almostperfectly to the viewer without being diffracted again by the gratingsin the optically diffractive device 598. In some implementations, thelight from the illuminator 596 can be incident on the opticallydiffractive device 598 with a large incident angle from a side of thedisplay 594, such that the illuminator 596 does not block the viewer'sview and is not intrusive into the holographic light field 599. Theincident angle can be a positive angle or a negative angle with respectto a normal line of the display 594. For illustration, the incidentangle is presented as a positive angle. For example, the incident anglecan be in a range from 70 degrees to 90 degrees, e.g., in a range from80 degrees to 90 degrees. In a particular example, the incident angle is84 degrees. The diffracted light from the optically diffractive device598 can be diffracted at close to normal incidence into the display 594,such that the light can uniformly illuminate the display 594 and can bediffracted back near-normally through the optically diffractive device598 to the viewer's eyes with minimized power loss due to undesiredreflections, diffractions, and/or scatterings within or at the surfacesof the optically diffractive device 598. In some examples, thediffracted angle from the optically diffractive device 598 to thereflective display 594 can be in a range of −10° (or 10 degrees) to 10°(or 10 degrees), e.g., from −7° to 7°, or from 5° to 7°. In a particularexample, the diffracted angle is 6°. In another example, the diffractedangle is 0°.

In some implementations, as illustrated in FIG. 5H, the opticallydiffractive device 598 is arranged in front of the reflective display594, e.g., along the Z direction towards the viewer. The opticallydiffractive device 598 can include a field grating structure 598-1positioned on a substrate 598-2. A back surface of the field gratingstructure 598-1 faces a front surface of the reflective display 594, anda front surface of the field grating structure 598-1 is attached to thesubstrate 598-2. The light from the illuminator 596 can be incident onthe front surface of the field grating structure 598-1 through thesubstrate 598-2, e.g., from a side surface of the substrate 598-2. Forexample, the substrate 598-2 can have a wedged side surface, e.g., asillustrated with further details in FIG. 12C, such that the light at alarge incident angle can have less reflection loss.

As discussed with further details below, if a diffraction efficiency ofa diffractive structure, e.g., a holographic grating, is less than 100%,light incident at an incident angle can be diffracted by the diffractivestructure into zero and first orders. Light of first order (or firstorder light) is diffracted by the diffractive structure at a diffractedangle towards the display to therein diffract again to reconstruct aholographic light field 599. The first order can be also called firstdiffraction order. Light in the zero order (or zero order light, orundiffracted light, or the undiffracted order) is undiffracted (orundeflected) by the diffractive structure and transmitted by thediffractive structure at an angle corresponding to the incident angle.The zero order light may cause an undesired effect such as a ghostimage, e.g., when the zero order light is incident upon the reflectivedisplay 598-1 directly or subsequent to reflection off surfaces withinthe optically diffractive device 598.

To eliminate the undesired effect, the field grating structure 598-1 canbe spaced from the display 594. In some implementations, a back surfaceof the field grating structure 598-1 is spaced from a front surface ofthe display 594 by a gap. The gap can have any suitable distance, e.g.,1 mm. The gap can be filled with air or any lower-refractive-indexmaterial to satisfy total internal reflection (TIR) on an interface. Forexample, air has a refractive index (e.g., n≈1.0) which is much smallerthan that of a back layer of the field grating structure 598-1 (e.g.,n≈1.5), and hence any residual light at the incident angle (e.g., >70°)can be totally internally reflected by the back surface of the fieldgrating structure 598-1 when the incident angle is larger than acritical angle (e.g., for ≈41.8° for n≈1.5). That is, the residual lightat the incident angle cannot reach the reflective display 594 to causethe undesired effect. In some examples, at least one of the frontsurface of the reflective display 594 or the back surface of the fieldgrating structure 598-1 is treated with an anti-reflection coating,which can substantially reduce a part of the holographic light fieldreflected from the reflective display 594 back towards the reflectivedisplay 594 from the back of the field grating structure 598-1 whichotherwise could cause further ghost images. In some examples, the backsurface of the field grating structure 598-1 can be protected by anadditional layer, e.g., a glass layer.

In some implementations, instead of being spaced with a gap, the backsurface of the field grating structure 598-1 can be attached to thefront surface of the reflective display 594 using an intermediate layer.The intermediate layer can be an optically clear adhesive (OCA) layerwith a refractive index substantially lower than that of the back layerof the field grating structure 598-1, such that total internalreflection (TIR) can occur and the residual zero order light can betotally reflected at the interface between the intermediate layer andthe back layer of the field grating structure 598-1 back into theoptically diffractive structure 598.

In some implementations, the field grating structure 598-1 and thedisplay 594 can be separated with a gap so that any residual lightcannot reach the display 594. The gap can be filled with any suitabletransparent material, index-matching fluid, or OCA. In someimplementations, the field grating structure 598-1 can be formed in acover layer (e.g., a cover glass) of the display 594.

In some cases, to illuminate a whole surface of the reflective display594 by light diffracted from an active area of the field gratingstructure 598-1, the active area of the field grating structure 598-1can be no smaller than an area of the whole surface of the reflectivedisplay 594. In some implementations, the field grating structure 598-1and the reflective display 594 have a rectangular shape with a heightalong the X direction and a width along the Y direction. The active areaof the field grating structure 598-1 can have a height no smaller than aheight of the reflective display 594 and a width no smaller than a widthof the reflective display 594. If there is a substantial gap between thefield grating structure 598-1 and the reflective display 594, the fieldgrating structure 598-1 and the substrate 598-2 can be enlarged furtherso that an expanding cone (or frustrum) of light from the reflectivedisplay 594, e.g., the holographic light field 599, can be seen throughthe front of the optically diffractive device 598 over an entirevertical and horizontal field of view (around the +Z axis) of theholographic light field 599. The substrate 598-2 can be a little widerand higher than the field grating structure 598-1.

As light is incident on the field grating structure 598-1 at asubstantially off-axis angle in a dimension, e.g. the Z direction, thelight can be narrower by the cosine of the incidence angle in thatdimension. The light from the illuminator 596 can have a narrowrectangular shape incident into the field grating structure 598-1 whichcan then expand the light to a large rectangular shape incident into thereflective display 594. One or more optical components, e.g., mirrors,prisms, optical slabs, and/or optical fillers, can be arranged betweenand within the illuminator 596, the optically diffractive structure 598,and the reflective display 594 to further expand the light and to filterits bandwidth. In some examples, the expanded light can have a beam areasomewhat smaller than the active area of the reflective display 594,such that the edges and surrounding area of the illuminated area of thereflective display 594 are not noticeable in reflection or scattertowards the viewer. In some examples, the expanded light can have a beamarea somewhat larger than the active area of the reflective display 594,such that the edges of the illuminated area of the reflective display594 are fully illuminated even if the edges of the expanded light arenot uniform, e.g. because of diffraction off masking edges.

In some implementations, the controller 592 can obtain graphic dataincluding respective primitive data for a plurality of primitivescorresponding to an object in a three-dimensional space, determine, foreach of the plurality of primitives, an electromagnetic (EM) fieldcontribution to each of a plurality of display elements of thereflective display 594, generate, for each of the plurality of displayelements, a sum of the EM field contributions from the plurality ofprimitives to the display element, and generate, for each of theplurality of display elements, the respective control signal based onthe sum of the EM field contributions to the display element.

In some implementations, the illuminator 596 can include one or morecolor light emitting elements, e.g., red, blue, or green color lasers(or LEDs), configured to emit light of corresponding colors. Theoptically diffractive device 598 can be configured to diffract aplurality of different colors of light at respective diffracted anglesthat are substantially identical to each other. Each of the respectivediffracted angles can be in a range of 0° to ±10°, e.g., substantiallyidentical to 0°, + or −1°, + or −2°, + or −3°, + or −4°, + or −5°, + or−6°, + or −7°, + or −8°, + or −9°, or + or −10°.

In some implementations, the controller 592 is configured tosequentially modulate the display 594 with information associated with aplurality of colors of light in a series of time periods. For example,the information can include a series of color holograms or color images.The controller 592 can control the illuminator 596 to sequentially emiteach of the plurality of colors of light to the optically diffractivedevice 598 during a respective time period of the series of timeperiods, such that each of the plurality of colors of light isdiffracted by the optically diffractive device 598 to the reflectivedisplay 594 and diffracted by modulated display elements of thereflective display 594 to form a respective color three-dimensionalholographic light field 599 corresponding to the object during therespective time period. Depending on temporal coherence-of vision effectin an eye of a viewer, the plurality of colors can be combined in theeye to give an appearance of full color. In some cases, the illuminator596 is switched off among different light emitting elements during astate change of the display image (or holographic reconstruction) suchas during black-insertion subframes between color subframes or duringblanking or retrace periods of a video source or during LC rise, fall,or DC-balancing inversion transitions, or during system warm-up, or whenthe intended holographic light field is completely black, or during acalibration procedure, and is switched on when a valid image (orholographic reconstruction) is presented for a period of time. This canalso rely on persistence of vision to make the image (or holographicreconstruction) appear stable and flicker-free.

If a part of the holographic light field 599 appears in front of thedisplay 594, as illustrated by a light field 599-1 in FIG. 5H, that partof the holographic light field 599 is a real part of the reconstructedimage or holographic reconstruction (also called a real image or a realholographic reconstruction). When a viewer sees a point of light infront of the display 594, there really is light being reflected from thedisplay 594 to that point. If a part of the light field 599 appears tothe viewer to be behind (or inside) the display 594, as illustrated by alight field 599-2 in FIG. 5H, that part of the holographic light field599 is a virtual part of the reconstructed image or holographicreconstruction (also called a virtual image or a virtual holographicreconstruction). When the viewer sees a point of light which appears tobe behind or inside the display 594, there is actually no light beingdiffracted from the display 594 to that virtual point: rather, part ofthe light diffracted from the display 594 appears to be originated atthat virtual point.

The computer 591 and/or the controller 592 can be configured to adjust acomputation (e.g., by equations) of the information (e.g., atwo-dimensional hologram, image, or pattern) to be modulated in thedisplay 594 to move the reconstructed holographic light field 599 backand forth along a direction (e.g., the Z direction) normal to thedisplay 594. The computation can be based on a holographic renderingprocess, e.g., as illustrated in FIGS. 2 and 3A-3G. In some cases, theholographic light field 599 can be fully in front of the display 594. Insome cases, the holographic light field 599 can appear to be all behindthe display 594. In some cases, as illustrated in FIG. 5H, theholographic light field can have one part in front of the display 594,e.g., the real part 599-1, and another part appearing to be behind thedisplay, e.g., the virtual part 599-2. That is, the light field 599 canappear to straddle a surface of the display 594, which can be calledimage planning.

The optically diffractive device 598 can be implemented in differentconfigurations. In some implementations, the optically diffractivedevice 598 includes a holographic grating, e.g., a Bragg grating, for aparticular color, e.g., as illustrated in FIGS. 7A, 7B, and 8, and theholographic light field 599 can correspond to the particular color. Insome implementations, the optically diffractive device 598 includesmultiple holographic gratings for different colors in a single recordinglayer, e.g., as illustrated in FIGS. 7C, 7D and 7E.

In some implementations, the optically diffractive device 598 includesmultiple holographic gratings for different colors in differentrecording layers, e.g., as illustrated in FIGS. 9A to 12C. Asillustrated in FIG. 7F, a grating for a particular color can diffractnot only light of the particular color, but also light of other colors,which can cause crosstalk among the different colors. In some examples,as described with further details below with respect to FIGS. 9A to 10B,the optically diffractive device 598 can include multiple holographicgratings with one or more color-selective polarizers to suppress (e.g.,eliminate or minimize) color crosstalk. In some examples, as describedwith further details below with respect to FIGS. 11 to 12C, theoptically diffractive device 598 can include multiple holographicgratings with one or more reflective layers for light of differentcolors incident at respective incident angles to suppress colorcrosstalk and zero order light. In some examples, the opticallydiffractive device 598 can include multiple holographic gratings withone or more color-selective polarizers, e.g., as illustrated in FIGS. 9Ato 10B, and one or more reflective layers, e.g., as illustrated in FIGS.11 to 12C, to suppress color crosstalk and zero order diffraction. Eachof the color-selective polarizers can be configured for a single coloror multiple colors. Each of the reflective layers can be configured fora single color or multiple colors.

FIG. 5I illustrates another system 590A with a reflective display 594Awith optically diffractive illumination using an optically diffractivedevice 598A. The reflective display 594A can be the same as thereflective display 594 of FIG. 5H. Different from the opticallydiffractive device 598 of the system 590 of FIG. 5H, the opticallydiffractive device 598A of the system 590A has a reflective fieldgrating based structure that can include a reflective field gratingstructure 598-1A and a substrate 598-2A. The substrate 598-2A can be aglass substrate. The reflective field grating structure 598-1A caninclude one or more reflective holographic gratings for one or moredifferent colors. The reflective field grating structure 598-1A isarranged on a front surface of the substrate 598-2A, e.g., along Zdirection. An illuminator 596 is arranged behind the reflective fieldgrating structure 598-1A and configured to illuminate light on thereflective field grating structure 598-1A at a large incident angle. Thelight is diffracted back (along −Z direction) to the reflective display594A that further diffracts the light back through the opticallydiffractive device 598A to form a holographic light field 599.

FIG. 5J illustrates another system 590B with a transmissive display 594Bwith optically diffractive illumination using an optically diffractivedevice 598B. The transmissive display 594B can be the same as thetransmissive display 534 of FIG. 5C, 544 of FIG. 5D, or 564 of FIG. 5E.Similar to the optically diffractive structure 598A of FIG. 5I, theoptically diffractive structure 598B can be a reflective field gratingbased structure that can include a reflective field grating structure598-1B and a substrate 598-2B. The substrate 598-2B can be a glasssubstrate. The reflective field grating structure 598-1B can include oneor more reflective holographic gratings for one or more differentcolors. Different from the optically diffractive structure 598A of FIG.5I, the reflective field grating structure 598-1B in the opticallydiffractive structure 598B is arranged on a back surface of thesubstrate 598-2B. An illuminator 596 is arranged before the reflectivefield grating structure 598-1B and configured to illuminate light on thereflective field grating structure 598-1B at a large incident angle. Thelight is diffracted back (along −Z direction) to the transmissivedisplay 594B that further diffracts the light to form a holographiclight field 599.

FIG. 5K illustrates another system 590C with a transmissive display 594Cwith optically diffractive illumination using an optically diffractivedevice 598C. The transmissive display 594C can be the same as thetransmissive display 594C of FIG. 5J. Similar to the opticallydiffractive structure 598 of FIG. 5H, the optically diffractivestructure 598C can be a transmissive field grating based structure thatcan include a transmissive field grating structure 598-1C and asubstrate 598-2C. The substrate 598-2C can be a glass substrate. Thetransmissive field grating structure 598-1C can include one or moretransmissive holographic gratings for one or more different colors.Different from the optically diffractive structure 598 of FIG. 5H, thetransmissive field grating structure 598-1C in the optically diffractivestructure 598C is arranged on a front surface of the substrate 598-2C.An illuminator 596 is arranged behind the transmissive field gratingstructure 598-1C and configured to illuminate light on the transmissivefield grating structure 598-1C at a large incident angle. The light isdiffracted forward (along +Z direction) to the transmissive display 594Cthat further diffracts the light to form a holographic light field 599.

As discussed above, FIGS. 5H to 5K show different combinations ofreflective/transmissive displays and reflective/transmissive fieldgrating based optically diffractive devices. In some cases, placing anoptically diffractive device on a rear side of a display can providebetter protection for photopolymers if the photopolymers have notalready been protected by their inherent structures or by additionalglass layers. In some cases, a transmissive grating can be mechanicallyand optically closer to a display, and light from the transmissivegrating to the display can travel a shorter distance, than from areflective grating, which can reduce alignment, coverage, dispersion,and/or scatter issues. In some cases, transmissive gratings can have agreater wavelength tolerance and a lesser angular tolerance thanreflective gratings. In some cases, transmissive grating can be lesslikely to mirror ambient illumination towards a viewer, e.g., ceilinglights and illuminated keyboards. In some cases, with a transmissivedisplay, a viewer can get closer to the display, and the holographiclight field may be projected closer to the display. In some cases, for atransmissive display, a glass substrate for the transmissive display canhave a proven manufacturing capability up to >100″ diagonal withnear-seamless tiling for cinema and architectural sizes. In some cases,reflective and transflective displays can embed a controller, e.g.,Maxwell holography circuitry, behind display elements, and transmissivedisplays can incorporate the controller or circuitry behind inter-pixel(or inter-phasel) gaps. In some cases, reflective and transflectivedisplays can enable light to double-pass display elements (e.g., liquidcrystal material) and can have twice the refractive index change oftransmissive displays that uses a single-pass through the liquid crystalmaterial. A transflective display can represent a display with anoptical layer that reflects transmitted light.

Exemplary Display Implementations

As noted above, a display in Maxwell holography can be a phasemodulating device. A phase element of the display (or a display element)can be represented as a phasel. For illustration only, a liquid crystalon silicon (LCOS) device is discussed below to function as the phasemodulating device. The LCOS device is a display using a liquid crystal(LC) layer on top of a silicon backplane. The LCOS device can beoptimized to achieve minimum possible phasel pitch, minimum cross-talkbetween phasels, and/or a large available phase modulation or retardance(e.g., at least 2π).

A list of parameters can be controlled to optimize the performance ofthe LCOS device, including a birefringence of LC mixture (Δn), a cellgap (d), a dielectric anisotropy of the LC mixture (Δε), a rotationalviscosity of the LC mixture (η), and the maximum applied voltage betweenthe silicon backplane and a common electrode on top of the LC layer (V).

There can be a fundamental trade-off that exists between parameters ofthe liquid crystal material and structure. For example, a fundamentalbounding parameter is the available phase modulation or retardance (Re),which can be expressed as:

Re=4π·Δn·d/λ  (8),

where λ is the wavelength of an input light. If the retardance Re needsto be at least 2π for a red light with a wavelength of about 0.633 μm,then

n·d

0.317 μm  (9).

The above expression implies that there is a direct trade-off betweencell gap (d) and birefringence (

n) of the LC mixture for any given wavelength (λ).

Another bounding parameter is the switching speed, or the switching time(T) it takes for the liquid crystal (LC) molecules in an LC layer toreach the desired orientation after a voltage is applied. For example,for real-time video (˜60 Hz) using a 3-color field sequential colorsystem, a minimum of 180 Hz modulation of the LC layer is involved,which puts an upper bound on the LC switching speed of 5.6 milliseconds(ms). Switching time (T) is related to a number of parameters includingthe liquid crystal mixture, the cell gap, the operating temperature, andthe applied voltage. First, T is proportional to d². As the cell gap dis decreased, the switching time decreases as the square. Second, theswitching time is also related to the dielectric anisotropy (Δε) of theliquid crystal (LC) mixture, with a higher dielectric anisotropyresulting in a shorter switching time and a lower viscosity (which maybe temperature dependent) also resulting in a shorter switching time.

A third bounding parameter can be the fringing field. Due to the highelectron mobility of crystalline silicon, an LCOS device can befabricated with a very small phasel size (e.g., less than 10 μm) andwith submicron inter-phasel gaps. When the adjacent phasels are operatedat different voltages, the LC directors near the phasel edges aredistorted by the lateral component of the fringing field, whichsignificantly degrades the electro-optic performance of the device. Inaddition, as the phasel gap becomes comparable to the incident lightwavelength, diffraction effects can cause severe light loss. The phaselgap may need to be kept at less than or equal to a phasel pitch to keepphase noise within an acceptable level.

In some examples, the LCOS device is designed to have a phasel pitch of2 μm and a cell gap of approximately 2 μm if the fringe field boundingcondition is observed. According to the above expression

n·d

0.317 μm, hence Δn needs to be equal to 0.1585 or greater, which isachievable using current liquid crystal technology. Once the minimumbirefringence for a given phasel pitch is determined, the LC can beoptimized for switching speed, e.g., by increasing the dielectricanisotropy and/or decreasing the rotational viscosity.

Nonuniform Phasels Implementations for Displays

In an LCOS device, a circuit chip, e.g., a complementarymetal-oxide-semiconductor (CMOS) chip or equivalent, controls thevoltage on reflective metal electrodes buried below the chip surface,each controlling one phasel. A common electrode for all the phasels issupplied by a transparent conductive layer made of indium tin oxide onthe LCOS cover glass. The phasels can have identical sizes and sameshape (e.g., square). For example, a chip can have 1024×768 (or4096×2160) phasels, each with an independently addressable voltage. Asnoted above, when the inter-phasel gap becomes comparable to theincident light wavelength, diffraction effects can appear due to theperiodic structure of the LCOS device, which may cause severe light lossand a strong periodic structure in the diffracted light.

In Maxwell holographic calculations, each phasel receives a sum of EMcontributions from each primitive and is relatively independent fromeach other. Thus, the phasels of the LCOS device in Maxwell holographycan be designed to be different from each other. For example, asillustrated in FIG. 6A, the LCOS device 600 can be made of a number ofnonuniform (or irregular) phasels 602. At least two phasels 602 havedifferent shapes. The nonuniform shapes of the phasels 602 can greatlyreduce or eliminate diffractive aberrations (e.g., due to the periodicstructure in the diffracted light), among other effects, and thusimprove image quality. Although the phasels can have nonuniform shapes,the phasels can be designed to have a size distribution with an average(e.g., about 3 μm) that satisfies a desired spatial resolution. Thesilicon backplane can be configured to provide a respective circuit(e.g., including a metal electrode) for each of the phasels according tothe shape of the phasel.

In an array of phasels in an LCOS device, to select a specific phasel, afirst voltage is applied to a word line connecting a row of phaselsincluding the specific phasel and a second voltage is applied to a bitline connecting a column of phasels including the specific phasel. Aseach phasel has a resistance and/or a capacitance, the operational speedof the LCOS device can be limited by the switching (or rise and falltimes) of these voltages.

As noted above, in Maxwell holography, the phasels can have differentsizes. As illustrated in FIG. 6B, an LCOS device 650 is designed to haveone or more phasels 654 having a size larger than the other phasels 652.All of the phasels can still have a size distribution that satisfies thedesired resolution. For example, 99% of the phasels have a size of 3 μm,and only 1% of the phasels have a size of 6 μm. The larger size of thephasel 654 allows to arrange at least one buffer 660 in the phasel 654besides other circuitry same as in the phasel 652. The buffer 660 isconfigured to buffer the applied voltage such that the voltage is onlyapplied to a smaller number of phasels within a row or column ofphasels. The buffer 660 can be an analog circuit, e.g., made of atransistor, or a digital circuit, e.g., made of a number of logic gates,or any combination thereof.

For example, as illustrated in FIG. 6B, a voltage is applied to a wordline 651 and another voltage is applied to a bit line 653 to select aparticular phasel 652*. The phasel 652* is in the same row as the largerphasel 654 including the buffer 660. The voltage is mainly applied tothe first number of phasels in the row and before the larger phasel 654and obstructed by the buffer 660 in the larger phasel 654. In such away, the operational speed of the LCOS device 650 can be improved. Withthe larger size of the phasels 654, other circuitry can be also arrangedin the LCOS device 650 to further improve the performance of the LCOSdevice 650. Although the phasels 654 and the phasels 652 in FIG. 6B havesquare shape, the phasels can also have different shapes as illustratedin FIG. 6A as long as there are one or more phasels 654 having a largersize than the other phasels 652.

Exemplary Calibrations

The unique nature of Maxwell holography in the present disclosure allowsfor the protection of calibration techniques that can create asignificant competitive advantage in the actual production of highquality displays. A number of calibration techniques can be implementedto be combined with the Maxwell holographic computational techniques,including:

-   -   (i) using image sensors or light field sensors in conjunction        with a Dirichlet boundary condition modulator and/or in        conjunction with mechanical and software diffractive and        non-diffractive calibration techniques;    -   (ii) software alignments and software calibrations including        individual color calibrations and alignments with Dirichlet        boundary condition modulators; and    -   (iii) embedding silicon features in the boundary condition        modulators that allow for photo detection (including power and        color) and/or thermometry to be built directly into the        modulator that when combined with Maxwell holography creates a        powerful and unique approach to simplifying manufacturing        calibration processes.

In the following, for illustration only, three types of calibrations areimplemented for phase based displays, e.g., LCOS displays. Each phaseelement can be represented as a phasel.

Phase Calibration

An amount of phase added to light impinging upon an LCOS phase element(or phasel) can be known directly by a voltage applied to the LCOSphasel. This is due to the birefringent liquid crystal (LC) rotating inthe presence of an electric field and thus changing its index ofrefraction and slowing down light to alter its phase. The altered phasecan depend upon electrical characteristics of the liquid crystal (LC)and the silicon device in which the LC resides. Digital signals sent tothe LCOS need to be transformed into correct analog voltages to achievehigh quality holographic images. Phase calibration is involved for theLCOS device to ensure that a digital signal is properly transformed intoan analog signal applied to the LC such that it produces the greatestamount of phase range. This conversion is expected to result in a linearbehavior. That is, as the voltage is changed by fixed increments, thephase also changes by fixed increments, regardless of the startingvoltage value.

In some cases, an LCOS device allows a user to alter a digital-to-analogconverter (DAC) such that the user has a control over the amount ofanalog voltage output given a digital input signal. A digitalpotentiometer can be applied to each input bit. For example, if thereare 8 input bits, there can be 8 digital potentiometers corresponding toeach input bit. The same digital inputs from the digital potentiometerscan be applied to all phasels of the LCOS device. Bits set to “1”activate a voltage, and bits set to “0” do not activate the voltage. Allvoltages from such “1” bits are summed together to obtain the finalvoltage sent to each phasel. There may also be a DC voltage applied inall cases such that all “0” bits results in a baseline non-zero voltage.Thus, the phase calibration of the LCOS device can be implemented bysetting values of the digital potentiometers for the LCOS device. Forexample, as noted above, a controller can compute EM field contributionsfrom a list of primitives to each of phasels of a display, generate arespective sum of the EM field contributions from the primitives to eachof the phasels, and generate respective control signals to each of thephasels for modulating a phase of the phasel. The same digital inputsfrom the digital potentiometers can be applied to adjust the respectivecontrol signals to all of the phasels of the LCOS device, which isdifferent from a phasel-by-phasel based phase calibration. The digitalinputs can be set once for a duration of an operation of the LCOSdevice, e.g., for displaying a hologram.

To determine an optimal set of phase calibration values for the digitalinputs, a genetic algorithm can be applied, where there are many inputvalues that lead to one output value, such as phase range or holographicimage contrast. This output value can be reduced to one number known asthe fitness. The genetic algorithm can be configured to exploredifferent combinations of input values until it achieves an output withthe highest fitness. In some cases, the algorithm can take two or moreof the most fit inputs and combine a number of their constituent valuestogether to create a new input that has characteristics of the takeninputs but is different from each of the taken inputs. In some cases,the algorithm can alter one of these constituent values to something notfrom either of the taken fit inputs, which is represented as a“mutation” and can add a variety to the available fit inputs. In somecases, one or more optimal values can be found by taking advantage ofthe knowledge gained from prior measurements with good results whiletrying new values so the optimal values do not be restricted to a localmaximum.

There can be multiple ways to calculate the fitness output value. Oneway is to calculate the phase change of the light given a set of digitalinputs applied to all the phasels on the LCOS. In this scheme, theincident light can be polarized. Upon impinging upon the LCOS, theincident light's polarization can change depending on the rotation ofthe LC. The incident light can be diffracted back through anotherpolarizer set to either the same polarization or 90 degrees differentfrom the original polarization and then into a light detector.Therefore, when the LC rotation changes, the intensity as viewed fromthe light detector can change. Accordingly, the phase change of thelight can be perceived indirectly through the intensity variations.Another way to calculate the phase change is to measure the intensitydifference of a Maxwell holographic reconstruction from the background.This is most effective in a projective display. Measuring the intensityin such an instance may need the use of computer vision algorithms toidentify the Maxwell holographic reconstruction and measure itsintensity. Another way to determine the phase change is to measure orimage it microscopically in an interferometric optical geometry.

Alignment Calibration

Light sources and other optical elements may not be adequately alignedwithin a holographic device and therefore may need to be aligned.Different liquid crystals (LC) and optically diffractive elements ordiffractive optical elements can also behave differently for differentwavelengths of the light sources. Moreover, especially the LC,diffractives, and light sources can change device to device and overtime (aging and burn-in) and as a result of changes in the operatingenvironment such as the operating temperature and mechanically induceddeformation due to thermal or mechanical stress, giving differentcharacteristics, e.g., object scaling, to the same input hologram whenshown in a different base color or at a different time or in a differentenvironment. Furthermore, certain hardware features can apply differentoptical effects to the output light, e.g., lensing, that also may needcorrection under these circumstances.

In some implementations, the problems described above can be addressedby applying mechanical translations, deformations, and rotations to oneor more optical element. In some implementations, the problems describedabove can be addressed by applying a mathematical transform to a phasecalculated for a phasel of a display. The phase is a respective sum ofthe EM field contributions from a list of primitives to the phasel. Themathematical transform can be derived from a mathematical expression,e.g., a Zernike polynomial, and can be varied by altering polynomialcoefficients or other varying input values. The mathematical transformcan vary phasel-by-phasel as well as by color. For example, there is aZernike polynomial coefficient that corresponds to the amount of tilt tobe applied to the light after it diffracts off of the display.

To determine these coefficients/input values, a hardware and softwaresetup can be created where a 2D camera, a photometer, a light fieldcamera, and/or other photometric or colorimetric instrumentation ispointed at a reflective or diffusely transmissive surface illuminated bythe LCOS in the case of a projective display or pointed into the LCOS inthe case of a direct-view display. One or more holographic test patternsand objects can be sent to the display and measured by the measuringinstrument or instruments. 2D cameras or 3D (light field) cameras orcamera arrays can use machine vision algorithms to determine what isbeing displayed and then calculate its fitness. For example, if a gridof dots is the test pattern, then the fitness can be determined by astatistical measure of how close they are together, how centered theyare on their intended positions, how much distortion they exhibit (e.g.,scale or pincushion), etc. There can be different fitness values fordifferent performance characteristics. Depending on these values,corrections can be applied, e.g., in the form of changing coefficientsto the Zernike polynomial, until the fitness reaches a predeterminedsatisfactory level or passes a visual or task-oriented AB test. Thesetest patterns can be rendered at different distances to ensure thatalignment is consistent for objects at different distances, and not justat one 3D point or plane in particular. Such depth-based calibrationscan involve iterative processes that involve altering the depth of theholographic test pattern or elements therein, as well as the position ofthe reflective or diffusely transmissive surface, and where the previouscalibrations can be repeated until converging upon a solution that worksat multiple depths. Finally, white dots can be displayed to show theeffectiveness of the calibration.

Color Calibration

In displays, holographic or otherwise, it is important that, when anytwo units are rendering the same image, colors match between displaysand additionally match colors defined by television (TV) and computerdisplay standards, like the Rec.709 standard for high-definitiontelevision (HDTV) or the sRGB color space of computer monitors.Different batches of hardware components, e.g., LEDs and laser diodes,can exhibit different behaviors for the same inputs and can outputdifferent colors when perceived by the human eye. Therefore, it isimportant to have a color standard to which all display units can becalibrated.

In some implementations, an objective measurement of color specified bymeasurements of intensity and chromaticity can be obtained by measuringcolor intensity against Commission internationale de l'eclairage (CIE)Standard Observer curves. By requesting that each display reproduces asample set of known colors and intensities, then measuring the outputlight using a colorimeter device calibrated to the CIE Standard Observercurves, the color output of a device in a chosen CIE color space can beobjectively defined. Any deviation of the measured values from the knowngood values can be used to adapt the output colors on the display tobring it back into alignment or conformance, which can be implementedusing an iterative measure-adapt-measure feedback loop. Once a Maxwellholographic device produces accurate outputs for a given set of inputs,the final adaptations can be encoded as look-up tables for theilluminators that map input values to output intensities, and colormatrix transformations that transform input colors to output color spacevalues. These calibration tables can be embedded in the device itself toproduce reliable objective output colors. Multiple such tables can beprovided for each of a multitude of operating temperature ranges.Multiple such tables can be provided for each of a multitude ofdifferent regions of the active surface of the LCOS. Calibration valuescan be interpolated between tables for adjacent temperature rangesand/or adjacent surface regions.

Additionally, given an LCOS device with fine enough features to controldiffraction with sub-wavelength accuracy, there may be no need fortri-stimulus illumination (e.g., linear mixes of red, green, and blue),and the LCOS device can be illuminated with a single wide spectrum lightsource and selectively tune the phasels output to produce tri-, quad-,even N-stimulus output colors which, combined with spatial ditheringpatterns, can reproduce a more complete spectral output of a colorrather than the common tri-stimulus approximation. Given a sufficientlywide spectrum illuminator this allows Maxwell holography to produce anyreflected color that lies inside the spectral focus of the human visualsystem or outside the spectral focus for infrared (IR) or ultraviolet(UV) structured light.

Exemplary Holographic Gratings

FIGS. 7A-7F illustrate implementations of example holographic gratingsthat can be included in an optically diffractive device (or a lightguidedevice), e.g., the optically diffractive device 598 of FIG. 5H, 598A ofFIG. 5I, 598B of FIG. 5J, or 598C of FIG. 5K. FIGS. 7A and 7B illustraterecording and replaying a holographic grating in a recording medium witha single color. FIGS. 7C and 7D illustrate recording three differentcolor holographic gratings in a recording medium with three differentcolors of light (FIG. 7C) and replaying them with a single color oflight (FIG. 7D). FIGS. 7E and 7F illustrate replaying three differentcolor holographic gratings in a recording medium with three differentcolors of light, and FIG. 7F illustrates color crosstalk amongdiffracted light of different colors. Any one of a recording referencelight beam, a recording object light beam, a replaying reference lightbeam, and a diffracted light beam is a polarized light beam that can bes polarized or p polarized.

FIG. 7A illustrates an example of recording a holographic grating in arecording medium. The recording medium can be a photosensitive material,e.g., a photosensitive polymer or photopolymer, silver halide, or anyother suitable material. The recording medium can be arranged on asubstrate, e.g., a glass substrate. The substrate can be transparent ornot transparent during the recording. In some implementations, thephotosensitive material can be adhered to a carrier film, e.g., a TAC(cellulose triacetate) film. The photosensitive material with thecarrier film can be laminated on the substrate, with the photosensitivematerial between the carrier film and the substrate.

In transmission holography, a recording reference beam and a recordingobject beam are incident from the same side on a same region of therecording medium with a recording reference angle θ_(r) and a recordingobject angle θ_(o), respectively. Each of the reference and object beamscan start in air, pass through the photosensitive material, and thenpass on into and through the substrate, exiting into air. The recordingreference beam and the recording object beam have the same color, e.g.,green color, and same polarization state, e.g., s polarized. Both of thebeams can originate from a laser source with high spatial and temporalcoherence so that the beams interfere strongly to form a standingpattern where the beams overlap. Within the recording medium, thepattern is recorded as a fringe pattern, e.g., a grating, includingmultiple parallel interference planes, as illustrated as tilted solidlines in FIG. 7A, at a fringe tilt angle θ_(t) that satisfies thefollowing expression:

θ_(t)=(θ_(o)+θ_(r))/2  (10),

where θ_(t) represents the fringe tilt angle in the recording mediumduring recording, θ₀ represents the object angle in the recording mediumduring recording, and θ_(r) represents a reference angle in therecording medium during recording.

A fringe spacing (or fringe period) d on a surface of the recordingmedium can be expressed as:

d=λ _(record)(n sin θ_(record))  (11),

where λ_(record) represents a recording wavelength (in vacuo), nrepresents the refractive index of the medium surrounding the grating(e.g., air with n=1.0), θ_(record) represents the inter-beam angleduring recording and is identical to |θ_(o)−θ_(r)|, where θ₀ representsthe object incidence angle at a surface of the recording medium duringrecording and θ_(r) represents the reference incidence angle at thesurface of the recording medium during recording. In some cases, thefringe spacing d has a size similar to a wavelength of a recordinglight, e.g., 0.5 μm. Thus, the fringe pattern can have a frequencyf=1/d, e.g., about 2,000 fringes per mm. The thickness D of therecording medium can be more than one order of magnitude larger than thewavelength of the recording light. In some examples, the thickness ofthe recording medium D is about 30 times of the wavelength, e.g., about16.0+/−2.0 μm. The carrier film can have a thickness larger than therecording medium, e.g., 60 μm. The substrate can have a thickness morethan orders of magnitude larger than the recording medium, e.g., about1.0 mm.

After the fringe pattern or grating is recorded in the recording medium,the fringe pattern can be fixed in the recording medium, e.g., for theexample of a photopolymer by exposure of deep blue or ultraviolet (UV)light which can freeze the fringes in place and can also enhance thefringes' refractive index differences. The recording medium can shrinkduring the fixing. The recording medium can be selected to have a lowshrinkage during the fixing, e.g., less than 2% or such shrinkage can becompensated for.

As each beam passes through an interface between materials of differentrefractive indices, some portion of the beam is reflected followingFresnel's laws, which give the percentage of power reflected at eachtransition. The reflection is polarization dependent. For light at asmaller incidence angle, e.g., 30°, the Fresnel reflections can beweaker. For light at a larger incident angle (e.g., 80°) and fors-polarized light, the Fresnel reflections can be stronger. When theincident angle reaches or is beyond a critical angle, total internalreflection (TIR) occurs, that is, the reflectivity is 100%. For example,from a transition from glass (n=1.5) to air (n=1.0), the critical angleis about 41.8°. Since the refractive index is dependent on polarizationand weakly dependent on wavelength, reflected powers at large angles ofincidence can become weakly wavelength dependent, and can becomestrongly polarization dependent.

FIG. 7B illustrates an example of diffracting a replay reference beam bythe grating of FIG. 7A. For transmission holography, during replay thesubstrate is transparent. The substrate can be also an optically clearplastic, such as TAC or some other low-birefringence plastic. When therecorded grating in the recording medium is thin compared with thewavelength of the replay reference beam, e.g., the thickness of therecording medium is less than one order of magnitude larger than thereplay wavelength, the grating's diffracted angle can be described by agrating equation as below:

mλ _(replay) =nd(sin θ_(in)−sin θ_(out))  (12),

where m represents a diffraction order (integer), n represents therefractive index of the medium surrounding the grating, d represents thefringe spacing on the surface of the recording medium, θ_(in) representsthe incident angle from the surrounding medium onto the grating, θ_(out)represents the output angle for the m^(th) order from the grating backinto the surrounding medium, and λ_(replay) represents the replaywavelength in vacuo.

When the recorded grating is comparatively thick, for example, when thethickness of the recording medium is more than one order of magnitude(e.g., 30 times) larger than the replay wavelength, the grating can becalled a volume grating or a Bragg grating. For volume gratings, Braggselectivity can strongly enhance diffraction efficiency at a Braggangle. The Bragg angle can be determined based on numerical solutions,e.g., rigorous couple-wave solutions, and/or experimentation anditeration. At off-Bragg angles, the diffraction efficiency can besubstantially decreased.

The Bragg condition can be satisfied when an angle of incident onto thefringe planes equals the diffraction angle off of the fringe planeswithin the medium containing the fringe planes. The grating equation(12) can then become Bragg's equation:

mλ _(replay)=2n _(replay)Λ_(replay) sin(θ_(m)−θ_(t))  (13),

where m represents the diffraction order (or Bragg order), n_(replay)represents the refractive index in the medium, Λ_(replay) represents thefringe spacing in the recording medium, θ_(m) represents the m^(th)Bragg angle in the recording medium, θ_(t) represents the fringe tilt inthe recording medium, and Λ_(replay) can be identical to d cos θ_(t).

The Bragg condition can be automatically satisfied for volume gratingsrecorded and replayed with the same angles and wavelengths (assuming noshrinkage during processing). For example, as illustrated in FIG. 7B, avolume grating is recorded and replayed with the same wavelength (e.g.,green color) and reference angle (e.g., Or), and the grating candiffract out a first order replay beam at the angle of the recordingobject beam. A fraction of the incident light beam can pass through thegrating as an undeflected or undiffracted zero order light beam. If thezero order light beam gets to a display such as a reflective LCOSdevice, the light beam can cause undesired effects, e.g., ghost images.

If the replay reference angle is not changed but the replay referencewavelength is changed, a diffraction efficiency η of a Bragg grating ina recording medium can be expressed as:

η∝2D _(replay) sin θ_(Bragg) ²λ cos θ_(tilt.replay)/(λ_(Bragg) ² cosθ_(Bragg))  (14),

where η represents diffraction efficiency, D_(replay) represents athickness of the recording medium (after shrinkage) during replay,θ_(Bragg) represents a replay reference angle (after shrinkage) at Braggfor an intended replay wavelength λ_(Bragg), δλ represents an error in areplay wavelength, that is, δλ=|λ_(replay)−λ_(Bragg)|, andθ_(tilt.replay) represents the fringe tilt in the recording mediumduring replay (after shrinkage). All λ are values in vacuo.

FIG. 7C illustrates an example of recording gratings for differentcolors in a recording medium using different colors of light. Asillustrated, three fringe patterns (or gratings) can be recorded in asingle recording medium, e.g., sequentially or simultaneously. A fringepattern corresponds to a replay color (e.g., red, green, or blue) andcan be recorded with a different wavelength. The recording referencebeam and the recording object beam have the same polarization state.Each beam can be s polarized. The recording reference beams for eachcolor can be incident upon the single recording medium at the samereference beam angle θ_(r) (e.g., +30°). The recording object beams foreach color can be incident upon the single recording medium at the sameobject beam angle θ₀ (e.g., −20°).

The fringe plane tilt θ_(t) for each grating during recording can be thesame, as θ_(t) is independent of wavelength, e.g.,θ_(t)=(θ_(o)+θ_(r))/2. The fringe spacing d perpendicular to the fringeplanes during recording can be different for each grating, as d dependson wavelength. In some examples, as illustrated in FIG. 7C, the fringespacings are in proportion red:green:blue≈123%:100%:89% corresponding toexample wavelengths of 640 nm:520 nm:460 nm.

FIG. 7D illustrates an example of recording gratings for differentcolors in a recording medium using a same color of light. Similar toFIG. 7C, three fringe patterns are recorded in a single photopolymer,one fringe pattern for each replay color. Different from FIG. 7C, thethree fringe patterns in FIG. 7D can be recorded using the samewavelength, e.g., green light. To achieve this, the recording objectbeams for each replay color can be incident upon the single recordingmedium at different object beam angles, and the recording referencebeams for each replay color can be incident upon the single recordingphotopolymer at different reference beam angles. The fringe tilt andfringe spacing in FIG. 7D for a replay color can match the fringe tiltand fringe spacing for that same replay color in FIG. 7C.

FIG. 7E illustrates an example of diffracting replay reference beams ofdifferent colors by gratings for different colors. The gratings can berecorded as illustrated in FIG. 7C or 7D. Similar to FIG. 7B, for areplay color, when the recording wavelength is the same as the replaywavelength and the replay reference angle is a first Bragg angle of agrating for the replay color, the grating diffracts a first order of thereplay reference beam at a diffracted angle identical to a recordingobject angle, and transmits a zero order of the replay reference beam atthe replay reference angle. Due to Bragg selectivity, the power of thereplay reference beam at the first order can be substantially largerthan the power of the replay reference beam at the zero order. The threereplay reference beams can have the same incident angles, e.g., 30°, andthe first order diffracted beams can have the same diffracted angles,e.g., 20°.

Replay reference angles for each color can be neither equal to oneanother, nor equal to the angles for the color used during recording.For example, for green color, a grating can be recorded at 532 nm, e.g.,using a high-power high-coherence green laser such as afrequency-doubled diode-pumped YaG laser, and then be replayed at 520±10nm using a green laser diode. In some cases, the green laser having thewavelength of 532 nm can also be used to record the required fringepattern for replay using a cheap red laser diode at 640±10 nm. For bluecolor, a grating can be recorded at 442 nm using a HeCd laser, and bereplayed using a 460±2 nm blue laser diode.

FIG. 7F illustrates an example of crosstalk among diffracted beams ofdifferent colors. Despite Bragg selectivity, each color can alsoslightly diffract off the gratings recorded for each other color, whichmay cause crosstalk among these colors. Compare to FIG. 7E providingonly first order diffraction for a corresponding color, FIG. 7F providesthe first order diffraction of each color off each grating.

For example, as illustrated in FIG. 7F, red grating, green grating, andblue gratings for red, green, and blue colors are respectively recorded.When the red light is incident at the same reference angle 30° on thered grating, the diffracted angle of the red light at first order is20°; but when the red light is incident at the same reference angle 30°on the green grating, the diffracted angle of the red light at firstorder is 32°; and when the red light is incident at the same referenceangle 30° on the blue grating, the diffracted angle of the red light atfirst order is 42°. Thus, diffracted light can be present at unintendedangles, and color crosstalk occurs. Similarly, when the green light isincident at the reference angle 30° on the green grating, the diffractedangle of the green light at first order is 20°; but when the green lightis incident at the same reference angle 30° on the red grating, thediffracted angle of the green light at first order is 11°; and when thegreen light is incident at the same reference angle 30° on the bluegrating, the diffracted angle of the green light at first order is 27°.Thus, diffracted light can be present at unintended angles, and colorcrosstalk occurs. Similarly, when the blue light is incident at thereference angle 30° on the blue grating, the diffracted angle of theblue light at first order is 20°; but when the blue light is incident atthe same reference angle 30° on the red grating, the diffracted angle ofthe blue light at first order is 6°; and when the blue light is incidentat the same reference angle 30° on the green grating, the diffractedangle of the blue light at first order is 14°. Thus, diffracted lightcan be present at unintended angles, and color crosstalk occurs.Accordingly, when a single color of light, e.g., green light, isincident on the three gratings in the recording medium, the threegratings diffract the single color of light to have a first diffractedgreen light at a diffracted angle of 20°, a second diffracted greenlight at a diffracted angle of 27°, and a third diffracted green lightat a diffracted angle at 11°. The two unintended angles of each color ofdiffracted light can generate undesired effects.

In some cases, instead of recording the three different gratings forthree different colors in a single recording layer, the three differentgratings can instead be stored in three separated recording layers thatare stacked together. Similar to FIG. 7F, color crosstalk can occur whenthree colors of light are incident at the same incident angle on any oneof the gratings. Implementations of the present disclosure providemethods and devices for suppressing the color crosstalk in multiplegrating stacks, as illustrated with further details in FIGS. 9A to 12C.

FIG. 8 illustrates an example of recording a holographic grating with alarge reference angle in a recording medium. Using a large replayreference beam angle can allow a thin replay system. Also, a replayoutput beam, that is, the diffracted angle at first order, can be normalto a display. Thus, the recording object beam can be close to normalincidence, as illustrated in FIG. 8.

For Bragg diffraction, the Fresnel reflections for p- and fors-polarized light are both low at each fringe plane, but at an angle ofincidence of 45°, s polarization can be reflected orders of magnitudemore strongly than p polarization. Thus, if the incidence angle of thereplay reference on to the fringes in the recording medium is close to45°, then Bragg resonance off the fringes can be highly polarizationsensitive, strongly favoring s-polarization. The recording object beamcan be near normal incident on the recording medium, such that thereconstructed object beam or the diffracted replay beam can be at nearnormal incidence on a display. As the fringe tilt in the recordingmedium is the average of the in-medium recording object and referenceangles, to achieve, at replay, an incidence angle onto the fringes ofclose to 45° and hence high polarization selectivity, a recordingreference angle approaching 90° in the recording medium can be used. Aninterbeam angle between the recording object beam and recordingreference beam can be close to 90°. For example, the interbeam angle is84° as illustrated in FIG. 8, and the fringe tilt of the fringe planesin the recording beam is 42°, and the incident angle of the replayreference beam onto the fringe planes is 48°, which corresponds to apolarization sensitivity of about 90:1.

In some cases, to obtain a replay output (or first order) diffractedangle to be 0°, the recording object beam can be not identical to 0°,but close to 0°, which can be achieved by taking into consideration acombination of shrinkage of a recording medium during its processing anda slight wavelength difference between a recording wavelength and areplaying wavelength. For example, the recording object angle can be ina range from −10° to 10°, e.g., a range from −7° to 7°, or 5° to 7°. Insome examples, the recording object angle is 0°. In some examples, therecording object angle is 6°.

In some implementations, to achieve large enough interbeam angles, e.g.,close to 90°, during recording, a prism is applied such that eachrecording beam enters the prism through a prism face where its incidenceangle into the prism is close to the normal of that face of the prism,and thus refraction and Fresnel losses become both negligible. The prismcan be index matched to the recording medium's cover film or substrateat an interface, such that the index mismatch is negligible at theinterface, and refraction and Fresnel losses can be also negligible atthe interface.

Exemplary Optically Diffractive Devices

FIGS. 9A-12C show implementations of example optically diffractivedevices. Any one of the devices can correspond to, for example, theoptically diffractive device 598 of FIG. 5H or 598C of FIG. 5K. Theoptically diffractive devices are configured to individually diffractlight with a plurality of colors to suppress (e.g., reduce or eliminate)color crosstalk among diffracted light and/or to suppress zero orderundiffracted light. FIGS. 9A to 10B show example optically diffractivedevices including color-selective polarizers. The color-selectivepolarizers can selectively change a polarization of a selected color,such that a single color of light can have s polarization to achievehigh diffraction efficiency at first order while other colors of lighthave p polarization thus lower diffraction efficiency at the firstorder. FIGS. 11 to 12C show example optically diffractive devicesincluding reflective layers. The reflective layers can selectivelytotally reflect a single color of light of zero order while transmittingother colors of light.

Optically Diffractive Devices with Color-Selective Polarizers

FIG. 9A illustrates an example optically diffractive device 900including holographic gratings for two colors and correspondingcolor-selective polarizers, and FIG. 9B illustrates an example 950 ofdiffracting the two colors of light by the optically diffracted device900 of FIG. 9A. For illustration, the device 900 is configured for greenand blue colors of light.

The optically diffractive device 900 includes a first opticallydiffractive component 910 having a first diffractive grating (B grating)912 for blue color of light and a second optically diffractive component920 having a second diffractive grating (G grating) 922 for green colorof light. Each of the diffractive gratings can be between a carrierfilm, e.g., a TAC film, and a substrate, e.g., a glass substrate. Thecarrier film can be after the diffractive grating and the substrate canbe before the diffractive grating along the Z direction, or vice versa.As illustrated in FIG. 9A, the first optically diffractive component 910includes a substrate 914 and a carrier film 916 on opposite sides of theB grating 912, and the second optically diffractive component 920includes a substrate 924 and a carrier film 926 on opposite sides of theG grating 922. The optically diffractive device 900 can include a fieldgrating substrate 902 on which the first and second opticallydiffractive components 910 and 920 are stacked. An anti-reflection (AR)coating 901 can be attached to or applied on a surface of the fieldgrating substrate 902 to reduce reflection at the surface.

The optically diffractive device 900 can also include one or more layersof optically-clear index-matched adhesive (OCA), UV-cured or heat-curedoptical glues, optical contacting, or index matching fluid to attach orstick together adjacent layers or components, e.g., the field gratingsubstrate 902 and the BY filter 904, the BY filter 904 and the firstdiffractive component 910 (or the substrate 914), the first diffractivecomponent 910 (or the carrier film 916) and the GM filter 906, and/orthe GM filter 906 and the second diffractive components 920 (or thesubstrate 924). An order of the carrier film 914 or 924, the substrate916 or 926, and the OCA layers can be determined based on theirrefractive indices at a wavelength of a replay light to reducerefractive index mismatch at interfaces and thus reduce Fresnelreflections at the interfaces.

Each of the first and second diffractive gratings can be a holographicgrating (e.g., volume grating or Bragg grating) independently recordedand fixed (e.g., cured) in a recording medium, e.g., a photosensitivepolymer. A thickness of the recording medium can be more than one orderof magnitude larger than a recording wavelength, e.g., about 30 times.Similar to what is illustrated in FIG. 7A or FIG. 8, a recordingreference light beam incident at a recording reference angle and arecording object light beam incident at a recording object angle on therecording medium can interfere in the recording medium to form thediffractive grating. Then, similar to what is illustrated in FIG. 7B, areplaying reference light beam can be diffracted by the recordeddiffractive grating at first order and zero order. The recording lightbeams and the replaying light beam can have the same s polarizationstate. A replaying wavelength of the replaying light beam can besubstantially identical to a recording wavelength of the recording lightbeams.

In some examples, the replay incident angle can be substantiallyidentical to the recording reference angle (or a Bragg angle), and aBragg condition can satisfy. Light of first order (or first order light)is diffracted at a diffracted angle substantially close to the recordingobject angle, and light of zero order (or zero order light) isundiffracted and transmitted at the replay incident angle. Due to Braggselectivity, the power of the first order light can be substantiallyhigher than the power of the zero order light. The power of the zeroorder light (e.g., residual light or depleted light) depends on thediffraction efficiency of the diffractive grating. The higher thediffraction efficiency is, the lower the power of the zero order lightis. In some examples, the recording reference angle, the recordingobject angle, the replay incident angle, the recording wavelength, andthe replay wavelength can be configured such that the replay outputangle (or diffracted angle at first order) is substantially close to 0°or normal to the grating. The diffracted angle can be in a range of −10°to 10°, e.g., in a range of −7° to 7°, 0° to 10°, or 5° to 7°. In aparticular example, the diffracted angle is 6°.

Also, due to polarization sensitivity, the diffraction efficiency for spolarized light of a first color (e.g., blue color) incident at a replayreference angle and diffracted with first order at the diffracted anglecan be substantially higher than the diffraction efficiency for ppolarized light of the same color incident at the replay reference anglediffracted with first order at the diffracted angle. As illustrated inFIG. 7F, a second color of light (e.g., green color) incident at thesame replay incident angle as the first color of light is diffracted ata diffraction angle different from the diffraction angle of the firstcolor of light. Thus, due to both Bragg sensitivity and polarizationsensitivity, the diffraction efficiency for the first color of lightincident in s polarization state at the reply incident angle anddiffracted with first order can be substantially higher than thediffraction efficiency for the second color of light incident in ppolarization state at the same replay incident angle or at a differentreplay incident angle.

The optically diffractive device 900 can be configured to suppresscrosstalk between diffracted light beams of blue and green colors. Forexample, when the B grating 912 is positioned in front of the G grating922 in the device 900 along the Z direction, light is incident on the Bgrating 912 prior to being incident on the G grating 922. The opticallydiffractive device 900 can be configured such that blue color of lightis incident on the B grating 912 in s polarization state and the greencolor of light is incident on the B grating 912 in p polarization stateand the green color of light is incident on the G grating 922 in spolarization state. In some cases, the optically diffractive device 900can also be configured such that the residual blue color of light isincident on the G grating 922 in p polarization state.

In some implementations, as shown in FIGS. 9A and 9B, the opticallydiffractive device 900 can include a color-selective polarizer 906 (alsoknown as a color-selective retarder or filter) between the firstdiffractive grating 912 and the second diffractive grating 922 (orbetween the first diffractive component 910 and the second diffractivecomponent 920). The color-selective polarizer 906 can include a GMfilter configured to rotate a polarization state of green color of lightby 90 degrees, e.g., from p polarization state to s polarization state,but without rotation of a polarization state of blue color of light.

In some implementations, as shown in FIGS. 9A and 9B, the opticallydiffractive device 900 can include another color-selective polarizer 904in front of the first diffractive grating 912 and the second diffractivegrating 922 along the Z direction. The color-selective polarizer 904 caninclude a BY filter configured to rotate a polarization state of bluecolor of light by 90 degrees from p polarization state to s polarizationstate, but without rotation of a polarization state of green color oflight.

As shown in FIGS. 9A and 9B, both blue color of light 952 and greencolor of light 954 can be incident in p polarization state,simultaneously or sequentially, into the optically diffractive device900. The two colors of light can have a same incident angle θ°. When theblue color of light 952 and the green color of light 954 are firstincident on the BY filter 904, the color-selective polarizer 904 rotatesthe p polarization state of the blue color of light to s polarizationstate, without rotation of the polarization state of the green color oflight, such that the blue color of light is incident on the B grating912 in s polarization state and the green color of light is incident onthe B grating 912 in p polarization state. The B grating 912 diffractsthe blue color of light in s polarization state into first order bluecolor of light 952′ at a diffracted angle with a first diffractionefficiency and transmits zero order blue color of light 952″ at theincident angle. Due to polarization sensitivity and Bragg sensitivity,the B grating 912 diffracts the green color of light 954 in ppolarization state with a diffraction efficiency substantially smallerthan the first diffraction efficiency, and most of the green color oflight 954 in p polarization state transmits through the B grating 912.The color-selective polarizer 906 rotates p polarization state of thegreen color of light into s polarization state, without rotation of spolarization state of the blue color of light, such that the G grating922 diffracts the green color of light in s polarization into firstorder green color light 954′ at a diffracted angle with a seconddiffraction efficiency and transmits zero order green color of light954″ at the incident angle. Thus, the diffracted blue color of light952′ and green color of light 954′ exit out of the optically diffracteddevice 900 with the same s polarization state and with the samediffracted angle, e.g., in a range from −10° to 10° or −7° to 7°, orsubstantially close to 0° or normal to the device 900.

As shown in FIG. 5H, the optically diffractive device 900 can bepositioned in front of a cover glass 930 of a display, e.g., the display594 of FIG. 5H, along the Z direction. As discussed above in FIG. 5H,the optically diffractive device 900 can be attached to the cover glass930 with an OCA layer or index-matching oil, or spaced with a gap suchas an air gap. The diffracted blue color of light 952′ and green colorof light 954′ can be incident in the same s polarization state and atthe same incident angle (e.g., at substantially normal incidence) intothe display. The display can diffract the blue color of light 952′ andthe green color of light 954′ back into and through the opticallydiffractive device 900. The blue color of light and green color of lightdiffracted from the display cannot significantly be further diffractedby the optically diffractive device 950 as they are incident on thediffractive gratings 912 and 922 at an angle far off-Bragg.

The display 594 can be illuminated by light polarized in a direction ofthe display's alignment layer or a direction perpendicular to thedisplay's alignment layer. The display can be rotated in its own planebetween horizontal and vertical orientations, hence which polarizationis required depends on which orientation the display is in. In someimplementations, the display can be illuminated with p polarized light.The blue color of light and green color of light diffracted from theoptically diffractive device 900 can be incident in the same ppolarization state on the display. The optically diffractive device 900can include an additional color-selective polarizer after the G grating922 to rotate the s polarization state of each of the blue color oflight 952′ and the green color of light 954′ to p polarization state.

In some implementations, the blue color of light is incident in spolarization state and the green color of light is incident in ppolarization state into the optically diffractive device 900, and theoptically diffractive device 900 can include no BY filter 904 before theB grating 912 to rotate the polarization state of the blue color oflight.

In some implementations, the zero order undiffracted (or transmitted)blue color of light and/or the zero order undiffracted (or transmitted)green color of light can be totally internally reflected by one or morereflective layers arranged in the optically diffractive device 900, asdiscussed with further details in FIGS. 11 to 12C.

FIG. 10A illustrates an example optically diffractive device 1000,including holographic gratings for three colors and correspondingcolor-selective polarizers, for individually diffracting the threecolors of light. FIG. 10B illustrates an example of diffracting thethree colors of light by the optical device of FIG. 10A. Compared toFIGS. 9A and 9B, the optically diffractive device 1000 includes anadditional diffractive component for an additional color and differentcolor-selective polarizers for the three colors. For illustration, thedevice 1000 is configured for blue, red, and green colors of light.

As illustrated in FIG. 10A, the optically diffractive device 1000 can bearranged in front of a cover glass 1050 of a display, e.g., the display594 of FIG. 5H, along the Z direction. The optically diffractive device1000 includes a first diffractive component 1010, a second diffractivecomponent 1020, and a third diffractive component 1030 that can besequentially stacked together on a field grating substrate 1002 alongthe Z direction. An AR film 1001 can be applied to or coated on a frontsurface of the field grating substrate 1002 to reduce reflection oflight. Each of the first, second, and third diffractive components 1010,1020, 1030 can include a respective substrate 1014, 1024, 1034, arespective diffractive grating 1012, 1022, 1032, and a respectivecarrier film 1016, 1026, 1036. The respective diffractive grating 1012,1022, 1032 is between the respective substrate 1014, 1024, 1034 and therespective carrier film 1016, 1026, 1036. In some cases, the respectivesubstrate 1014, 1024, 1034 is in front of the respective carrier film1016, 1026, 1036 along the Z direction. In some cases, the respectivecarrier film 1016, 1026, 1036 is in front of the respective substrate1014, 1024, 1034 along the Z direction.

Each of the first, second, and third diffractive gratings 1012, 1022,and 1032 can be configured to: diffract a single color of light in spolarization state incident at an incident angle with a diffractionefficiency substantially higher, e.g., more than one order of magnitude,two orders of magnitude, or three orders of magnitude, than adiffraction efficiency where the diffractive grating diffracts anothercolor of light in p polarization state incident at a same or differentincident angle. Each of the first, second, and third diffractivegratings 1012, 1022, and 1032 can be a holographic grating, e.g., avolume grating or a Bragg grating. Each of the first, second, and thirddiffractive gratings 1012, 1022, and 1032 can be independently recordedand fixed in a recording medium, e.g., a photosensitive polymer or aphotopolymer.

The optically diffractive device 1000 can include multiplecolor-selective polarizers for the three colors of light. In someimplementations, a BY filter 1004 is between a field grating substrate1002 and the first diffractive grating 1012 of the first diffractivecomponent 1010 and configured to rotate a polarization state of bluecolor of light, without rotation of a polarization state of each of redand green colors of light. A MG filter 1006 is between the first andsecond diffractive gratings 1012 and 1022 (or between the first andsecond diffractive components 1010 and 1020) and configured to rotate apolarization state of each of blue and red colors of light, withoutrotation of a polarization state of green color of light. A YB filter1008 is between the second and third diffractive gratings 1022 and 1032(or between the second and third diffractive components 1020 and 1030)and configured to rotate a polarization state of each of red and greencolors of light, without rotation of a polarization state of blue colorof light. An MG filter 1040 is after the third diffractive grating 1032(or the third diffractive component 1030) and configured to rotate apolarization state of each of red and blue colors of light, withoutrotation of a polarization state of green color of light.

In some implementations, a color-selective polarizer is composed of twoor more sub-polarizers. The sub-polarizers can be arranged in anydesired order. For example, the YB filter 1008 can be composed of a RCfilter 1008-1 and a GM filter 1008-2. The RC filter 1008-1 can bearranged before the GM filter 1008-2, or vice versa. The RC filter1008-1 is configured to rotate a polarization state of red color oflight, without rotation of a polarization state of each of green andblue colors of light, and the GM filter 1008-2 is configured to rotate apolarization state of green color of light, without rotation of apolarization state of each of red and blue colors of light.

Adjacent layers or components in the optically diffractive device 1000can be attached together using one or more intermediate layers of OCA,UV-cured or heat-cured optical glues, optical contacting, or indexmatching fluid. As discussed in FIG. 5H, the optically diffractivedevice 1000 can be attached to the display cover glass 1050 through anintermediate layer or spaced with a gap, e.g., an air gap.

The optically diffractive device 1000 is configured to diffract thethree colors of light (red, green, and blue) out at a same diffractedangle (e.g., substantially normal incidence) with a same polarizationstate (e.g., s or p) towards the display. The three colors of light canbe input into the optically diffractive device 1000 at a same incidentangle θ°, e.g., substantially identical to be a Bragg angle. In somecases, the three colors of light can be incident at different angles tomatch a Bragg angle of each color's grating. The three colors of lightcan be in beams large enough to illuminate the whole region of thegratings. The three colors of light can be input into the opticallydiffractive device 1000 in a same polarization state (e.g., s or p). Insome cases, a color of light is incident from an opposite side (e.g., at−0°) or from the Y direction. Each color grating can be rotated to matchthe direction of its corresponding color replay reference light. Acorresponding color-selective polarizer can be independent of therotation of the color grating.

FIG. 10B illustrates an example 1060 of diffracting the three colors oflight (blue, red, green) by the optically diffractive device 1000 ofFIG. 10A. The three colors of light are incident into the opticallydiffractive device 1000 at the same incident angle θ° and in the same ppolarization state.

As shown in FIG. 10B, the BY filter 1004 rotates the p polarizationstate of the blue color of light to s polarization state, withoutrotation of the p polarization state of each of the red and green colorsof light. The B grating 1012 diffracts the blue color of light in the spolarization state into first order at the diffracted angle and zeroorder at the incident angle. The green and red colors of light incidentin p polarization state at the incident angle transmit through the Bgrating 1012.

The MG filter 1006 rotates the s polarization state of the blue color oflight to p polarization state, and the p polarization state of the redcolor of light to s polarization state, without rotation of the ppolarization state of the green color of light. The R grating 1022diffracts the red color of light in the s polarization state into firstorder at the diffracted angle and zero order at the incident angle. Theresidual blue color of light at zero order and the green color of lightincident in p polarization state at the incident angle transmit throughthe R grating 1022.

The RC filter 1008-1 in the YB filter 1008 rotates the s polarizationstate of the red color of light top polarization state, without rotationof the p polarization state of each of the green and blue colors oflight. The GM filter 1008-2 of the YB filter 1008 rotates the ppolarization state of the green color of light to s polarization state,without rotation of the p polarization of each of the red and bluecolors of light. The residual blue color of light at zero order, theresidual red color of light at zero order, and the green color of lighttransmit through the RC filter 1008-1 and the GM filter 1008-2.

The G grating 1032 diffracts the green color of light in the spolarization state into first order at the diffracted angle and zeroorder at the incident angle. The residual blue color of light and theresidual red color of light incident in p polarization state at theincident angle transmit through the G grating 1032.

The MG filter 1040 rotates the p polarization state of each of the redand blue colors of light to s polarization state, without rotation ofthe s polarization state of the green color of light. The diffractedblue, red, and green colors of light in the s polarization state at thesame diffracted angle propagate out of the optically diffractive device1000. The residual blue color of light, the residual red color of light,and the residual green color of light at zero order are also in spolarization state and at the incident angle transmit through the MGfilter 1040.

In some implementations, the optically diffractive device 1000 can havea larger size than the display. The residual blue, red, green colors oflight at zero order can propagate at a large angle out of the device1000 and into air. In some implementations, as discussed with furtherdetails below in FIGS. 11 to 12C, the optically diffractive device 1000can include one or more reflective layers between or after diffractivegratings for total internal reflection of corresponding colors of lightat zero order.

Exemplary Optically Diffractive Devices with Reflective Layers

FIGS. 11 to 12C show example optically diffractive devices includingreflective layers. The reflective layers can selectively totally reflecta single color of light at zero order while transmitting other colors oflight. Each of the optically diffractive devices includes multiplegratings each for a different color of light. Each color of light can beincident at a different replay reference angle on a correspondinggrating, such that each color of light undiffracted (or transmitted) bythe grating at zero order undergoes total internal reflection (TIR) froman interface subsequent to the grating which diffracts out the color oflight at first order at a same diffracted angle (e.g., substantiallynormal), but prior to the subsequent gratings (if any) in the device.The other colors of light can transmit at the corresponding replayreference angles through the grating.

FIG. 11 illustrates an example optically diffractive device 1100,including diffractive gratings for two colors and correspondingreflective layers, for individually diffracting the two colors of light.For illustration, the device 1100 is configured for green and bluecolors of light.

The optically diffractive device 1100 includes a first diffractivecomponent 1110 having a first diffractive grating 1112 for blue colorand a second diffractive component 1120 having a second diffractivegrating 1122 for green color. Each of the first and second diffractivegratings 1112, 1122 can be a holographic grating, e.g., a Bragg gratingor a volume grating. Each of the first and second diffractive gratings1112 and 1122 can be independently recorded and fixed in a recordingmedium, e.g., a photosensitive material such as a photopolymer.

The first diffractive component 1110 and the second diffractivecomponent 1120 can be stacked together on a field grating substrate 1102along a direction, e.g., the Z direction. The field grating substrate1102 can be an optically transparent substrate, e.g., a glass substrate.The optically diffractive device 1100 can be in front of a display suchas LCOS, e.g., the display 594 of FIG. 5H. For example, the opticallydiffractive device 1100 can be arranged on a cover glass 1130 of thedisplay through an intermediately layer or spaced by a gap, e.g., an airgap.

Similar to the first and second diffractive components 910, 920 in FIGS.9A and 9B, each of the first and second diffractive components 1110 and1120 can include a respective substrate 1114, 1124 and a respectivecarrier film 1116, 1126 on opposite sides of the respective diffractivegrating 1112, 1122. The respective diffractive grating 1112, 1122 isbetween the respective substrate 1114, 1124 and the respective carrierfilm 1116, 1126. The respective substrate 1114, 1124 and the respectivecarrier film 1116, 1126 can be arranged in an order to reduce refractiveindex mismatch and thus undesired Fresnel reflection. The respectivesubstrate 1114, 1124 can be a glass substrate that can have a refractiveindex same as or close to the refractive index of the field gratingsubstrate 1102. The respective carrier film 1116, 1126 can be a TACfilm. The TAC film can have a lower refractive index than aphotosensitive polymer used to record diffractive gratings 1112 and1122. In some examples, the respective substrate 1114, 1124 is arrangedbefore the carrier film 1116, 1126.

Adjacent layers or components in the optically diffractive device 1100can be attached together using one or more intermediate layers of OCA,UV-cured or heat-cured optical glues, optical contacting, or indexmatching fluid. For example, the first diffractive component 1110 (e.g.,the substrate 1114) can be attached to the field grating substrate 1102through an intermediate layer 1101, e.g., an OCA layer. The first andsecond diffractive components 1110 and 1120, e.g., the carrier film 1116and the substrate 1124, can be attached together through anotherintermediate layer 1103, e.g., an OCA layer. The optically diffractivedevice 1100 (e.g., the carrier film 1126) can be attached to the coverglass 1130 of the display through an intermediate layer 1105, e.g., anOCA layer.

As shown in FIG. 11, each of the first and second diffractive gratings1112, 1122 is configured to diffract a corresponding color of lightincident at a respective incident angle into first order at a respectivediffracted angle and zero order at the respective incident angle, andtransmit another color of light at a different incident angle, e.g., dueto Bragg selectivity. Thus, there can be no crosstalk between thedifferent colors of light individually diffracted at correspondingdiffractive gratings. Each color of light can be polarized. Thepolarization state of the different colors of light diffracted at firstorder can be the same, e.g., s or p. The respective diffracted anglesfor the different colors of light can be same, e.g., substantiallynormal.

The optically diffractive device 1100 can include a first reflectivelayer (or blocking layer) between the first grating 1112 and the secondgrating 1122. The first grating 1112 is configured to diffract bluecolor of light incident at a first incident angle θ_(b), e.g., 78.4°,into first order at a diffracted angle, e.g., 0° and zero order at thefirst incident angle. The first reflective layer, e.g., a refractiveindex of the first reflective layer, is configured to totally reflectthe blue color of light diffracted at the first incident angle but totransmit the green color of light incident at a second incident angleθ_(g), e.g., 76.5°. For example, the refractive index of the firstreflective layer is lower than the refractive index of a layerimmediately before the first reflective layer, e.g., the first grating1112. The first reflective layer can be a suitable layer between thefirst grating 1112 and the second grating 1122. In some examples, thefirst reflective layer is the carrier film 1116, as shown in FIG. 11.

Similarly, the optically diffractive device 1100 can include a secondreflective layer after the second grating 1112 and before the displaycover glass 1130. The second grating 1112 is configured to diffractgreen color of light incident at the second incident angle θ_(g), e.g.,76.5°, into first order at a diffracted angle, e.g., 0° and zero orderat the second incident angle. The second reflective layer, e.g., arefractive index of the second reflective layer, is configured tototally reflect the green color of light diffracted at the secondincident angle. The second reflective layer can be a suitable layerbetween the second grating 1122 and the cover glass 1130. In someexamples, the second reflective layer is the intermediate layer 1105, asshown in FIG. 11.

The totally reflected blue and green colors of light by thecorresponding reflective layers are reflected back into the opticallydiffractive device 1100 to a side of the optically diffractive device1100. As illustrated in FIG. 11, a surface of the side can be coatedwith an optical absorber 1104, e.g., a black coating, to absorb thetotally reflected blue and green colors of light diffracted at zeroorder by the corresponding diffractive gratings.

The field grating substrate 1102 can be thick enough such that thereplay reference light beams of different colors can enter at its edgeof the field grating substrate 1102. The field grating substrate 1102can be also configured to fully contain the replay reference light beamssuch that a viewer or observer cannot insert a finger or other objectinto the replay reference light beams. The viewer thus cannot obstructthe replay reference light beams, which can improve laser safety as theviewer cannot get an eye (or a reflective or focusing element) into thefull-power replay reference light beams. The optically diffractivedevice 1100 with the field grating substrate 1102 can be significantlymore compact than if the replay reference light beams are incident uponthe front surface of the optically diffractive device 1100 from air.

As the blue and green colors of light are incident at a relatively largereplay reference angle (or incident angle), e.g., more than 70°, Fresnelreflection can be significant from layer interfaces (for both P and Spolarization), and can rapidly increase with increasing replay referenceangle. Since the optically diffractive device 1100 contains a number ofinterfaces between materials of different refractive indices, theFresnel reflection losses from each such interface can add tosubstantially attenuate the replay output light, causing a substantiallyreduced replay-light power at each diffractive grating, especially thegrating, e.g., the G grating 1122, closest to the display. In someexamples, a replay reference angle (or an incident angle) for aparticular color of light can be selected to be just large enough toreliably undergo TIR, but not much large so that the Fresnel losses canbe reduced.

FIGS. 13A-13C illustrate relationships between diffracted (solid lines)and reflected or blocked (dashed lines) replay reference beam powerswith different incident angles for blue color of light (FIG. 13A), greencolor of light (FIG. 13B), and red color of light (FIG. 13C). Thediffracted replay reference beam power can be an illumination beam intoa cover glass of a display, e.g., the display 594 of FIG. 5H, adjacentto an optically diffractive device, e.g., the optically diffractivedevice 598 of FIG. 5H.

As illustrated in FIG. 13A, for blue color of light, plot 1302 shows thediffracted replay reference beam power (or the display's blueillumination power) as a replay reference beam angle (e.g., an incidentangle in glass) is increased, and plot 1304 shows the reflected replayreference beam power from a corresponding reflective layer as the replayreference beam angle is increased. As illustrated in FIG. 13B, for greencolor of light, plot 1312 shows the diffracted replay reference beampower (or the display's green illumination power) as a replay referencebeam angle (e.g., an incident angle in glass) is increased, and plot1314 shows the reflected replay reference beam power from acorresponding reflective layer as the replay reference beam angle isincreased. As illustrated in FIG. 13C, for red color of light, plot 1322shows the diffracted replay reference beam power (or the display's redillumination power power) as a replay reference beam angle (e.g., anincident angle in glass) is increased, and plot 1324 shows the reflectedreplay reference beam power from a corresponding reflective layer as thereplay reference beam angle is increased.

Replay reference angles for different colors of light can be chosen tobe large enough such that for each color of light, the correspondingreflective layer can totally reflect the color of light with areflection of 100%, while the replay reference angles can be smallenough such that the Fresnel losses do not substantially eliminate thediffracted replay reference beams or the illumination in the cover glassof the display. As an example, a diffraction efficiency of each gratingis 50% for blue, 60% for green, and 70% for red. A bottom layer of theoptically diffractive device is parallel to the cover glass of thedisplay. A diffracted angle of the replay object beam for each color is−6°. As shown in FIGS. 13A, 13B, 13C, the net object beam powers insidethe cover glass of the display are 46.8% for blue, 33.1% for green, and43.0% for red, when the replay reference angle is 78.4° for blue colorof light at 460 nm, 76.5° for green color of light at 520 nm, and 73.5°for red color of light at 640 nm.

FIG. 12A illustrates an example optically diffractive device 1200,including diffractive gratings for three colors and correspondingreflective layers, for individually diffracting the three colors oflight. For illustration, the device 1200 is configured for blue, greenand red colors of light.

The optically diffractive device 1200 includes a first diffractivecomponent 1210 having a first diffractive grating 1212 for blue color, asecond diffractive component 1220 having a second diffractive grating1222 for green color, and a third diffractive component 1230 having athird diffractive grating 1232 for red color. Each of the first, second,and third diffractive gratings 1212, 1222, 1232 can be a holographicgrating, e.g., a Bragg grating or a volume grating. Each of the first,second, and third diffractive gratings 1212, 1222, and 1232 can beindependently recorded and fixed in a recording medium, e.g., aphotosensitive material such as a photopolymer.

The first, second, and third diffractive components 1210, 1220, and 1230can be stacked together on a field grating substrate 1202 along adirection, e.g., the Z direction. The field grating substrate 1202 canbe an optically transparent substrate, e.g., a glass substrate. Theoptically diffractive device 1210 can be in front of a display such asLCOS, e.g., the display 594 of FIG. 5H. For example, the opticallydiffractive device 1200 can be arranged on a cover glass 1240 of thedisplay through an intermediately layer or spaced by a gap, e.g., an airgap.

Similar to the first, second, and third diffractive components 1010,1020, 1030 in FIGS. 10A and 10B, each of the first, second, and thirddiffractive components 1210, 1220, 1230 can include a respectivesubstrate 1214, 1224, 1234 and a respective carrier film 1216, 1226,1236 on opposite sides of the respective diffractive grating 1212, 1222,1232. The respective diffractive grating 1212, 1222, 1232 is between therespective substrate 1214, 1224, 1234 and the respective carrier film1216, 1226, 1236. The respective substrate 1214, 1224, 1234 and therespective carrier film 1216, 1226, 1236 can be arranged in an order toreduce refractive index mismatch and thus Fresnel reflection. Therespective substrate 1214, 1224, 1234 can be a glass substrate that canhave a refractive index same as or close to the refractive index of thefield grating substrate 1202. The respective carrier film 1216, 1226,1236 can be a TAC film. The TAC film can have a lower refractive indexthan a photosensitive polymer. In some examples, the respectivesubstrate 1214, 1224 is arranged before the carrier film 1216, 1226. Thesubstrate 1234 is arranged after the carrier film 1236.

Adjacent layers or components in the optically diffractive device 1100can be attached together using one or more intermediate layers of OCA,UV-cured or heat-cured optical glues, optical contacting, or indexmatching fluid. For example, the first diffractive component 1210 (e.g.,the substrate 1214) can be attached to the field grating substrate 1202through an intermediate layer 1201, e.g., an OCA layer. The first andsecond diffractive components 1210 and 1220, e.g., the carrier film 1216and the substrate 1224, can be attached together through anotherintermediate layer 1203, e.g., an OCA layer. The second and thirddiffractive components 1220 and 1230, e.g., the carrier film 1226 andthe carrier film 1236, can be attached together through anotherintermediate layer 1205, e.g., an OCA layer. The optically diffractivedevice 1200 (e.g., the substrate 1234) can be attached to the coverglass 1240 of the display through an intermediate layer 1207, e.g., anOCA layer.

As shown in FIG. 12A, each of the first, second, and third diffractivegratings 1212, 1222, 1232 is configured to diffract a correspondingcolor of light incident at a respective incident angle into first orderat a respective diffracted angle and zero order at the respectiveincident angle, and transmit another color of light at a differentincident angle, e.g., due to Bragg selectivity. Thus, there can be no orlittle crosstalk between the different colors of light individuallydiffracted at corresponding diffractive gratings. Each color of lightcan be polarized. The polarization state of the different colors oflight diffracted at first order can be the same, e.g., s or p. Therespective diffracted angles for the different colors of light can besame, e.g., substantially normal.

As discussed above in FIGS. 13A, 13B, 13C, different incident anglesθ_(b), θ_(g), θ_(r) (or replay reference angles) for different colors oflight (blue, green, and red) can be chosen, e.g., to be 78.4°, 76.5°,and 73.5°. The optically diffractive device 1200 can include a firstreflective layer (or blocking layer) between the first grating 1212 andthe second grating 1222. The first grating 1212 is configured todiffract blue color of light incident at the first incident angle θ_(b)into first order at a diffracted angle, e.g., 0°, and zero order at thefirst incident angle. The first reflective layer, e.g., a refractiveindex of the first reflective layer, is configured to totally reflectthe blue color of light diffracted at the first incident angle but totransmit the green color of light incident at the second incident angleθ_(g) and the red color of light incident at the third incident angleθ_(r). For example, the refractive index of the first reflective layeris lower than the refractive index of a layer immediately before thefirst reflective layer, e.g., the first grating 1212. The firstreflective layer can be a suitable layer between the first grating 1212and the second grating 1222. In some examples, the first reflectivelayer is the carrier film 1216, as shown in FIG. 12A. Total internalreflection occurs on an interface between the first grating 1212 and thecarrier film 1216. The totally reflected blue color of lightundiffracted (or transmitted) at the zero order is reflected back to thelayers above the first reflective layer and can be absorbed by anoptical absorber 1204 coated on a side surface of the opticallydiffractive device 1200.

The optically diffractive device 1200 can include a second reflectivelayer (or blocking layer) between the second grating 1222 and the thirdgrating 1232. The second grating 1222 is configured to diffract thegreen color of light incident at the second incident angle θ_(g) intofirst order at a diffracted angle, e.g., 0°, and zero order at thesecond incident angle. The second reflective layer, e.g., a refractiveindex of the second reflective layer, is configured to totally reflectthe green color of light diffracted at the second incident angle but totransmit the red color of light incident at the third incident angleθ_(r). For example, the refractive index of the second reflective layeris lower than the refractive index of a layer immediately before thesecond reflective layer. The second reflective layer can be a suitablelayer between the second grating 1222 and the third grating 1232. Insome examples, the second reflective layer is the intermediate layer1205, as shown in FIG. 12A. Total internal reflection occurs on aninterface between the carrier film 1226 and the intermediate layer 1205.The totally reflected green color of light undiffracted (or transmitted)at the zero order is reflected back to the layers above the secondreflective layer and can be absorbed by the optical absorber 1204.

The optically diffractive device 1200 can include a third reflectivelayer after the third grating 1232 and before the display cover glass1240. The third grating 1232 is configured to diffract the red color oflight incident at the third incident angle θ_(r) into first order at adiffracted angle, e.g., 0° and zero order at the third incident angle.The third reflective layer, e.g., a refractive index of the thirdreflective layer, is configured to totally reflect the red color oflight diffracted at the third incident angle. The third reflective layercan be a suitable layer between the third grating 1232 and the coverglass 1240. In some examples, the third reflective layer is theintermediate layer 1207 between the substrate 1234 and the cover glass1240, as shown in FIG. 12A. The totally reflected red color of lightundiffracted (or transmitted) at the zero order is reflected back to thelayers above the second reflective layer and can be absorbed by theoptical absorber 1204.

The field grating substrate 1202 can be thick enough such that thereplay reference light beams of different colors entering at its edge ofthe field grating substrate 1202. The field grating substrate 1202 canbe also configured to fully contain the replay reference light beamssuch that a viewer or observer cannot insert a finger or other objectinto the replay reference light beams. The viewer thus cannot obstructthe replay reference light beams, which can improve laser safety as theviewer cannot get an eye (or a reflective or focusing element) into thefull-power replay reference light beams. The optically diffractivedevice 1200 with the field grating substrate 1202 can be significantlymore compact than if the replay reference light beams are incident uponthe front surface of the optically diffractive device 1200 from air.

As shown in FIG. 12A, the field grating substrate 1202 can have arectangular cross-section in the XZ plane. The different colors of lightare incident from a side surface of the field grating substrate 1202.FIG. 12B illustrates another example optically diffractive device 1250including a wedged field grating substrate 1252. A wedged angle betweena side surface (or an input surface for light beams) 1251 of thesubstrate 1252 and a top layer 1253 of the substrate 1252 can beselected, and/or the side face can be AR coated, such that an opticalpath taken by any light beam returning to the field grating substrate1252 from the optically diffractive device 1250 and the display can beconveniently blocked or attenuated or directed to reduce or eliminatereflections back into the optically diffractive device 1250 and thedisplay. The optically diffractive device 1250 can include acorresponding optical absorber 1254 coated on an opposite side surface,which can be shorter than the optical absorber 1204 of FIG. 12A.

FIG. 12C illustrates a further example optically diffractive device 1270including a field grating substrate 1272 having a wedged input face1271. The wedged input face 1271 may be configured to reduce Fresnellosses of input light of different colors. The wedged input face 1271may be configured such that the input light of different colors isincident on the input face 1271 at substantially normal incidence andincident on corresponding diffractive gratings at different incidentangles (or replay reference angles). The wedged input face 1271 may beconfigured to refract input light of different colors to the desiredangles of each color inside the diffractive device and from convenientdirections and angles in air. For example, the wedged input face 1271may have a wedge angle such that the in air angles cause the input beamsto travel parallel to the front surface of the diffractive device orfrom the space behind the front surface of the diffractive device.

An AR coating can be formed on a front surface 1273 of the field gratingsubstrate 1272 to reduce or eliminate the reflection of ambient lightback towards a viewer. An AR coating can be also formed on a back faceof the optically diffractive device 1270 closest to the display toreduce or eliminate the undesirable reflection of light reflected and/ordiffracted from the display towards the viewer.

In some implementations, one or more layers in an optically diffractivedevice, e.g., the optically diffractive device 1100 of FIG. 11, 1200 ofFIG. 12A, 1250 of FIG. 12B, or 1270 of FIG. 12C, can be slightly wedged,which can allow fine tuning of TIR and Fresnel reflection at each layer.The layers can be also configured to reduce or eliminate a visibility ofNewton's rings or interference fringes which can occur between any pairof substantially parallel surfaces within the optically diffractivedevice when using narrow-band light sources, e.g., laser diodes.

Exemplary Fabrication Processes

FIG. 14A is a flowchart of an example process 1400 of fabricating anoptically diffractive device including diffractive structures andcorresponding color-selective polarizers. The optically diffractivedevice can be the optically diffractive device 598 of FIG. 5H, 598A ofFIG. 5I, 598B of FIG. 5J, or 598C of 5K, the optically diffractivedevice 900 of FIGS. 9A and 9B, or the optically diffractive device 1000of FIGS. 10A and 10B.

A first diffractive component for a first color is fabricated (1402).The first diffractive component can be the first diffractive component910 of FIGS. 9A and 9B or 1010 of FIGS. 10A and 10B. The firstdiffractive component includes a first diffractive structure, e.g., theB grating 912 of FIGS. 9A and 9B or the B grating 1012 of FIGS. 10A and10B, formed in a recording medium. The first diffractive structure isconfigured to diffract replay reference light of the first color (or thefirst color of light), which is incident in a first polarization stateat a first incident angle on the first diffractive structure, at a firstdiffracted angle with a first diffraction efficiency. The firstdiffraction efficiency can be substantially higher than a diffractionefficiency with which the first diffractive structure diffracts thefirst color of light or another different color of light incident in asecond polarization state different from the first polarization state atthe first incident angle, e.g., due to polarization selectivity. Thefirst polarization state can be s polarization, and the secondpolarization state can be p polarization.

The first diffractive structure can be a holographic grating, e.g., avolume grating or a Bragg grating. A thickness of the recording mediumcan be more than one order of magnitude larger than the wavelength ofthe first recording object beam, e.g., 30 times. In some examples, thefirst incident angle can be a Bragg angle. The first diffractionefficiency can be substantially higher than a diffraction efficiencywith which the first diffractive structure diffracts the first color oflight or another different color of light incident in the first orsecond polarization state at an incident angle different from the firstincident angle, e.g., due to Bragg selectivity.

The recording medium can include a photosensitive material, e.g., aphotosensitive polymer or photopolymer. The first diffractive structurecan be formed by exposing the photosensitive material to a firstrecording object beam at a first recording object angle andsimultaneously to a first recording reference beam at a first recordingreference angle. The first recording object beam and the first recordingreference beam can have a same wavelength, e.g., from a same lightsource, and the same first polarization state.

In some cases, the first color of light used for replay can include awavelength range wider than or identical to that of the first recordingreference beam or the first recording object beam. For example, thefirst recording reference beam and the first recording object beam canbe light beams of a laser, and the first color of light for replay canbe a light beam of a laser diode. In some cases, the first recordingreference beam and the first recording object beam can correspond to acolor different from the first color of the first color of light. Forexample, a green color laser light can be used to record a diffractivegrating for a red color.

The first incident angle of the first color of light can besubstantially identical to the first recording reference angle, and thefirst diffracted angle can be substantially identical to the firstrecording object angle. In some examples, the first recording referenceangle is in a range from 70 degrees to 90 degrees, e.g., in a range from80 degrees to 90 degrees. In some examples, the first recording objectangle is in a range from −10 degrees to 10 degrees, e.g., −7 degrees to7 degrees, 0 degrees or 6 degrees. In some examples, a sum of the firstrecording reference angle and the first recording object angle withinthe photosensitive material is substantially identical to 90 degrees.

The first diffractive structure can be fixed in the recording medium,e.g., by UV curing or heat curing. In some examples, the firstdiffractive component includes a carrier film, e.g., a TAC film, on therecording medium. In some examples, the first diffractive componentincludes a diffraction substrate, e.g., a glass substrate. The recordingmedium can be between a carrier film and a diffraction substrate.

A second diffractive component for a second color is fabricated (1404).The second diffractive component can be the second diffractive component920 of FIGS. 9A and 9B or 1020 of FIGS. 10A and 10B. The seconddiffractive component includes a second diffractive structure, e.g., theB grating 922 of FIGS. 9A and 9B or the R grating 1022 of FIGS. 10A and10B, formed in a second recording medium. The second diffractivestructure is configured to diffract replay reference light of the secondcolor (or the second color of light), which is incident in the firstpolarization state at a second incident angle on the second diffractivestructure, at a second diffracted angle with a second diffractionefficiency. The second diffraction efficiency can be substantiallyhigher than a diffraction efficiency with which the second diffractivestructure diffracts the second color of light or another different colorof light incident in the second polarization state at the secondincident angle or an incident angle different from the second incidentangle.

The second diffractive structure can be fabricated in a way similar tothe first diffractive structure as described above. The firstdiffractive structure and the second diffractive structure can beindependently fabricated. The second diffractive component can alsoinclude a carrier film and a diffraction substrate.

The first and second diffractive components can be configured such thatthe first diffracted angle and the second diffracted angle aresubstantially identical to each other, e.g., substantially normal. Thefirst incident angle and the second incident angle can be substantiallyidentical to each other.

A color-selective polarizer is arranged between the first and secondoptically diffractive components (1406). The color-sensitive polarizercan be the GM filter 906 of FIGS. 9A and 9B, or the MG filter 1006 ofFIGS. 10A and 10B. The optically diffractive structure can include afield grating substrate, e.g., the substrate 902 of FIGS. 9A and 9B orthe substrate 1002 of FIGS. 10A and 10B. The first optically diffractivecomponent, the color-selective polarizer, and the second opticallydiffractive component can be sequentially stacked on the field gratingsubstrate, such that the first color of light and the second color oflight are incident on the first optically diffractive component beforethe second optically diffractive component. The color-selectivepolarizer can be configured to rotate a polarization state of the secondcolor of light, e.g., from the second polarization state to the firstpolarization state, such that the second color of light can be incidentin the first polarization state on the second diffractive structure. Insome cases, the color-selective polarizer can rotate a polarizationstate of the first color of light. In some cases, the color-selectivepolarizer is configured not to rotate the polarization state of thefirst color of light.

In some implementations, an additional color-selective polarizer isarranged in front of the first diffractive component. For example, theadditional color-selective polarizer can be between the field gratingsubstrate and the first diffractive component. The additionalcolor-selective polarizer can be the BY filter 904 of FIGS. 9A and 9B orthe BY filter 1004 of FIGS. 10A and 10B. The additional color-selectivepolarizer is configured to rotate a polarization state of the firstcolor of light, e.g., from the second polarization state to the firstpolarization state, such that the first color of light is incident inthe first polarization state on the first diffractive structure. In somecases, the additional color-selective polarizer can rotate apolarization state of the second color of light, e.g., from the firstpolarization state to the second polarization state, such that thesecond color of light is incident in the second polarization state onthe first diffractive structure. In some cases, the additionalcolor-selective polarizer is configured not to rotate the polarizationstate of the second color of light, such that the second color of lightis incident in the second polarization state on the first diffractivestructure.

Adjacent components in the optically diffractive device can be attachedtogether through an intermediate layer. The intermediate layer can be anOCA layer, a UV-cured or heat-cured optical glue, optical contacting, oran index-matching fluid.

In some implementations, the process 1400 can further include forming athird optically diffractive component. The third diffractive componentincludes a third diffractive structure, e.g., the G grating 1032 ofFIGS. 10A and 10B, formed in a third recording medium. The thirddiffractive structure is configured to diffract replay reference lightof a third color (or the third color of light), which is incident in thefirst polarization state at a third incident angle on the thirddiffractive structure, at a third diffracted angle with a thirddiffraction efficiency. The third diffraction efficiency can besubstantially higher than a diffraction efficiency with which the thirddiffractive structure diffracts the third color of light or anotherdifferent color of light incident in the third polarization state at thesecond incident angle or an incident angle different from the thirdincident angle.

The third diffractive structure can be fabricated in a way similar tothe first diffractive structure as described above. The first, second,and third diffractive structures can be independently fabricated. Thethird diffractive component can also include a carrier film and adiffraction substrate. The first, second, and third diffractivecomponents can be configured such that the first, second, and thirddiffracted angles are substantially identical to each other, e.g.,substantially normal. The first, second, and third incident angles canbe substantially identical to each other.

A second color-selective polarizer can be arranged between the secondand third optically diffractive components. The second color-sensitivepolarizer can be YG filter of FIGS. 10A and 10B. The secondcolor-selective polarizer can be composed of two or more sub-polarizers,e.g., the RC filter 1008-1 and the GM filter 1008-2 of FIGS. 10A and10B. In some examples, the second color-selective polarizer is firstattached on the third diffractive component, and then the secondcolor-selective polarizer can be attached to the second diffractivecomponent. In some examples, the second color-selective polarizer can befirst attached to the second diffractive component, and then the thirddiffractive component can be attached to the second color-selectivepolarizer. The second color-selective polarizer can be configured torotate a polarization state of the third color of light from the secondpolarization state to the first polarization state, such that the thirdcolor of light is incident in the first polarization state on the thirddiffractive structure. The second color-selective polarizer can beconfigured to rotate the polarization state of the second color oflight, e.g., from the first polarization state to the secondpolarization state, without rotation of the polarization state of thefirst color of light.

A third color-selective polarizer can be arranged sequential to thethird optically diffractive component such that the third opticallydiffractive component is between the second and third color-selectivepolarizers. The third color-selective polarizer can be the MG filter1040 of FIGS. 10A and 10B. The third color-selective polarizer isconfigured to rotate the polarization state of each of the first andsecond colors of light, e.g., from the second polarization state to thefirst polarization state, without rotation of the first polarizationstate of the third color of light, such that the diffracted first,second, and third colors of light have the same polarization state.

FIG. 14B is a flowchart of an example process 1450 of fabricating anoptically diffractive device including diffractive structures andcorresponding reflective layers. The optically diffractive device can bethe optically diffractive device 598 of FIG. 5H, 598A of FIG. 5I, 598Bof FIG. 5J, or 598C of 5K, the optically diffractive device 1100 of FIG.11, or the optically diffractive device 1200 of FIG. 12A, 1250 of FIG.12B, or 1270 of FIG. 12C.

A first optically diffractive component is formed (1452). The firstdiffractive component can be the first diffractive component 1110 ofFIG. 11, 1210 of FIG. 12A, 12B, or 12C. The first diffractive componentincludes a first diffractive structure stored in a first recordingmedium. The first diffractive structure is configured to diffract afirst color of light incident at a first incident angle into first orderat a first diffracted angle and zero order at the first incident angle.A power of the first color of light at the first order can besubstantially higher than the power of the first color of light at zeroorder.

The first diffractive structure can be a holographic grating, e.g., avolume grating or a Bragg grating. A thickness of the recording mediumcan be more than one order of magnitude larger than the wavelength ofthe first recording object beam, e.g., 30 times. In some examples, thefirst incident angle can be a Bragg angle. The first diffractionefficiency can be substantially higher than a diffraction efficiencywith which the first diffractive structure diffracts the first color oflight or another different color of light incident at an incident angledifferent from the first incident angle, e.g., due to Bragg selectivity.Light incident at a different incident angle can transmit through thefirst diffractive structure.

The recording medium can include a photosensitive material, e.g., aphotosensitive polymer or photopolymer. The first diffractive structurecan be formed similar to step 1402 of FIG. 14A, e.g., by exposing thephotosensitive material to a first recording object beam at a firstrecording object angle and simultaneously to a first recording referencebeam at a first recording reference angle. The first recording objectbeam and the first recording reference beam can have a same wavelength,e.g., from a same light source, and the same polarization state. Thefirst incident angle of the first color of light can be substantiallyidentical to the first recording reference angle, and the firstdiffracted angle can be substantially identical to the first recordingobject angle. In some examples, the first recording reference angle isin a range from 70 degrees to 90 degrees, e.g., in a range from 70degrees to 80 degrees. In some examples, the first recording objectangle is in a range from −10 degrees to 10 degrees, e.g., −7 degrees to7 degrees, 0 degrees or 6 degrees. The first diffractive structure canbe fixed in the recording medium, e.g., by UV curing or heat curing. Insome examples, the first diffractive component includes a carrier film,e.g., a TAC film, on the recording medium. In some examples, the firstdiffractive component includes a diffraction substrate, e.g., a glasssubstrate. The recording medium can be between a carrier film and adiffraction substrate.

A second optically diffractive component is formed (1454). The seconddiffractive component can be the second diffractive component 1120 ofFIG. 11, 1220 of FIG. 12A, 12B, or 12C. The second diffractive componentincludes a second diffractive structure stored in a second recordingmedium. The second diffractive structure is configured to diffract asecond color of light incident at a second incident angle into firstorder at a second diffracted angle and zero order at the second incidentangle. A power of the second color of light at the first order can besubstantially higher than the power of the second color of light at thezero order.

The second diffractive structure can be fabricated in a way similar tothe first diffractive structure in step 1452. The first diffractivestructure and the second diffractive structure can be independentlyfabricated. The second diffractive component can also include a carrierfilm and a diffraction substrate.

The first and second diffractive components can be configured such thatthe first diffracted angle and the second diffracted angle aresubstantially identical to each other, e.g., substantially normal. Thefirst incident angle and the second incident angle are different fromeach other. The first and second incident angles can be determined,e.g., according to what is described in FIGS. 13A-13C. In some examples,the first color of light has a wavelength smaller than the second colorof light, and the first incident angle is larger than the secondincident angle.

A first reflective layer is arranged between the first and seconddiffractive structures (1456). The first reflective layer can be thereflective layer 1116 of FIG. 11, or 1216 of FIG. 12A, 12B, or 12C. Thefirst reflective layer is configured to totally reflect the first colorof light incident at the first incident angle, such that the first colorof light undiffracted (or transmitted) at the zero order can bereflected back into layers before the first reflective layer withoutpropagating to a display behind the optically diffractive device. Thefirst reflective layer can be configured to have a refractive indexsmaller than that of a layer of the first diffractive component that isimmediately adjacent to the first reflective layer, such that the firstcolor of light having the first incident angle is totally reflected byan interface between the first reflective layer and the layer of thefirst optically diffractive component, without totally reflecting thesecond color of light having the second incident angle. The firstreflective layer can be any suitable layer between the first and seconddiffractive structures. For example, the first reflective layer can bethe carrier film of the first diffractive component.

A second reflective layer is arranged behind the second diffractivestructures (1458). The second reflective layer can be the reflectivelayer 1105 of FIG. 11, or 1205 of FIG. 12A, 12B, or 12C. The secondreflective layer is configured to totally reflect the second color oflight incident at the second incident angle, such that the second colorof light undiffracted (or transmitted) at the zero order can bereflected back into layers before the second reflective layer withoutpropagating to the display behind the optically diffractive device.

An optical absorber can be formed on a side surface of the opticallydiffractive device. The optical absorber can be the optical absorber1104 of FIG. 11, 1204 of FIG. 12A, 12C, or 1254 of FIG. 12B. The opticalabsorber is configured to absorb the totally reflected light of thefirst and second colors.

In some implementations, a third optically diffractive componentincluding a third diffractive structure is formed. The third diffractivecomponent can be the third diffractive component 1230 of FIG. 12A, 12B,or 12C. The third diffractive structure can be the third diffractivestructure 1232 of FIG. 12A, 12B, or 12C. The third diffractive structureis configured to diffract a third color of light incident at a thirdincident angle into first order at a third diffracted angle and zeroorder at the third incident angle. A power of the third color of lightat the first order can be substantially higher than the power of thethird color of light at zero order. The first, second, and thirddiffracted angle can be substantially identical to each other. The thirdincident angle can be different from the first and second incidentangles. Each of the first and second reflective layers can be configuredto transmit the third color of light having the third incident angle.The second reflective layer can be arranged between the second and thirddiffractive structures. The third diffractive structure can befabricated in a way similar to the first diffractive structure in step1452. The first, second, and third diffractive structures can beindependently fabricated. The third diffractive component can alsoinclude a carrier film and a diffraction substrate.

A third reflective layer can be arranged behind the third diffractivestructure. The third reflective layer can be the third reflective layer1207 of FIG. 12A, 12B, or 12C. The third reflective layer is configuredto totally reflect the third color of light having the third incidentangle, such that the third color of light undiffracted (or transmitted)at zero order is reflected back to layers before the third reflectivelayer and can be absorbed by the optical absorber coated on the sidesurface of the optically diffractive device.

In some implementations, the first reflective layer includes a firstcarrier film of the first optically diffractive component. A seconddiffraction substrate of the second diffractive component is attached tothe first carrier film of the first diffractive component by a firstintermediate layer, e.g., an OCA layer. A second carrier film of thesecond diffractive component is attached to a third carrier film of thethird optically diffractive component by a second intermediate layer,and the second reflective layer can include the second intermediatelayer. The third reflective layer can be attached to a third diffractionsubstrate of the third diffractive component.

The process 1450 can include arranging the first diffractive componenton a substrate that is before the first diffractive component. Thesubstrate can be the field grating substrate 1102 of FIG. 11, 1202 ofFIG. 12A, 1252 of FIG. 12B, or 1272 of FIG. 12C. The substrate caninclude a front surface and a back surface. A front surface of the firstdiffractive component can be attached to the back surface of thesubstrate through a refractive index matching material or an OCA layer.

In some examples, the substrate includes a side surface angled to theback surface of the substrate, and the substrate is configured toreceive a plurality of different colors of light at the side surface.The substrate can be configured such that the plurality of differentcolors of light are incident on the side surface with an incident anglesubstantially identical to 0 degrees and incident on the back surface atrespective replay reference angles.

Implementations of the present disclosure can provide a method offabricating a device including an optically diffractive device and adisplay. The display can be the display 594 of FIG. 5H, 594A of FIG. 5I,594B of FIG. 5J, or 594 of FIG. 5K. The optically diffractive device canbe the optically diffractive device 598 of FIG. 5H, 598A of FIG. 5I,598B of FIG. 5J, or 598C of 5K the optically diffractive device 900 ofFIGS. 9A and 9B, the optically diffractive device 1000 of FIGS. 10A and10B, the optically diffractive device 1100 of FIG. 11, or the opticallydiffractive device 1200 of FIG. 12A, 1250 of FIG. 12B, or 1270 of FIG.12C.

The method can include forming the optically diffractive deviceaccording to the process 1400 of FIG. 14A or the process 1450 of FIG.14B. In some implementations, the optically diffractive device caninclude one or more color-selective polarizers and one or morereflective layers for a plurality of different colors of light. Theoptically diffractive device can be fabricated according to acombination of the process 1400 and the process 1450.

The method can further include arranging the optically diffractivedevice and the display, such that the optically diffractive device isconfigured to diffract the plurality of different colors of light to thedisplay.

In some implementations, the optically diffractive device and thedisplay can be arranged such that a back surface of the optical deviceis spaced from a front surface of the display by a gap, e.g., an airgap. The method can further include forming an anti-reflection coatingon at least one of the front surface of the display or the back surfaceof the optically diffractive device.

In some implementations, the optically diffractive device and thedisplay are arranged by attaching the back surface of the opticallydiffractive device on the front surface of the display through anintermediate layer. The intermediate layer can be configured to have arefractive index lower than a refractive index of a layer of theoptically diffractive device, such that each of the plurality ofdifferent colors of light diffracted at zero order by the opticallydiffractive device is totally reflected at an interface between theintermediate layer and the layer of the optically diffractive device.

The optically diffractive device is configured to diffract the pluralityof different colors of light at respective diffracted angles that aresubstantially identical to each other. Each of the respective diffractedangles can be in a range of −10 degrees to 10 degrees, e.g., −7 degreesto 7 degrees, 0 degrees, or 6 degrees. The display can be configured tore-diffract the diffracted colors of light back through the opticallydiffractive device. An area of the optically diffractive device cancover an area of the display. The optically diffractive device caninclude a substrate in front of the optical device that can beconfigured to receive the plurality of different colors of light at aside surface of the substrate that is angled to a back surface of thesubstrate.

Implementations of the present disclosure can provide a method ofoperating an optically diffractive device. The optically diffractivedevice can be the optically diffractive device 598 of FIG. 5H, 598A ofFIG. 5I, 598B of FIG. 5J, or 598C of 5K, the optically diffractivedevice 900 of FIGS. 9A and 9B, the optically diffractive device 1000 ofFIGS. 10A and 10B, the optically diffractive device 1100 of FIG. 11, orthe optically diffractive device 1200 of FIG. 12A, 1250 of FIG. 12B, or1270 of FIG. 12C. The optically diffractive device can be operated toconvert an incoming beam including a plurality of different colors oflight to individually diffracted colors of light,

Implementations of the present disclosure can provide a method ofoperating a system including an optically diffractive device and adisplay. The optically diffractive device can be the opticallydiffractive device 598 of FIG. 5H, 598A of FIG. 5I, 598B of FIG. 5J, or598C of 5K, the optically diffractive device 900 of FIGS. 9A and 9B, theoptically diffractive device 1000 of FIGS. 10A and 10B, the opticallydiffractive device 1100 of FIG. 11, or the optically diffractive device1200 of FIG. 12A, 1250 of FIG. 12B, or 1270 of FIG. 12C. The displayincludes a plurality of display elements. The display can be the display594 of FIG. 5H, 594A of FIG. 5I, 594B of FIG. 5J, or 594C of FIG. 5K.The method can be performed by a controller, e.g., the controller 112 ofFIG. 1A or 592 of FIG. 5H.

The method can include: transmitting at least one timing control signalto an illuminator to activate the illuminator to emit a plurality ofdifferent colors of light onto the optically diffractive device, suchthat the optically diffractive device converts the plurality ofdifferent colors of light to individually diffracted colors of light toilluminate the display and transmitting, for each of the plurality ofdisplay elements of the display, at least one respective control signalto modulate the display element, such that the individually diffractedcolors of light are reflected by the modulated display elements to forma multi-color three-dimensional light field corresponding to therespective control signals.

In some implementations, the method can further include: obtaininggraphic data comprising respective primitive data for a plurality ofprimitives corresponding to an object in a three-dimensional space,determining, for each of the plurality of primitives, an electromagnetic(EM) field contribution to each of the plurality of display elements ofthe display by calculating, in a three-dimensional coordinate system, anEM field propagation from the primitive to the display element,generating, for each of the plurality of display elements, a sum of theEM field contributions from the plurality of primitives to the displayelement, and generating, for each of the plurality of display elements,the respective control signal based on the sum of the EM fieldcontributions to the display element for modulation of at least oneproperty of the display element. The multi-color three-dimensional lightfield corresponds to the object.

In some implementations, the method include: sequentially modulating thedisplay with information associated with the plurality of differentcolors in a series of time periods, and controlling the illuminator tosequentially emit each of the plurality of different colors of light tothe optical device during a respective time period of the series of timeperiods, such that each of the plurality of different colors of light isdiffracted by the optical device to the display and reflected by themodulated display elements of the display to form a respective colorthree-dimensional light field corresponding to the object during therespective time period.

The plurality of different colors of light can be diffracted by theoptical device at a substantially same diffracted angle to the display.The diffracted angle can be within a range from 0 degrees to 10 degrees.

The illuminator and the optically diffractive device can be configuredsuch that the plurality of different colors of light are incident on thefirst optically diffractive component of the optically diffractivedevice with respective incident angles. Each of the respective incidentangles is in a range from 70 degrees to 90 degrees. In some cases, therespective incident angles are different from each other. In some cases,the respective incident angles are substantially identical to eachother.

An optically diffractive device can include a plurality of diffractivegratings for a plurality of different colors. The gratings can include atransmissive grating, a reflective grating, or a combination thereof.For example, each of the optically diffractive devices shown in FIGS. 9Ato 12C includes corresponding transmissive gratings for differentcolors. In some implementations, an optically diffractive device caninclude a combination of transmissive gratings and reflective gratingsthat can be configured for different colors. The optically diffractivedevice can be configured to diffract an incoming light towards a samedirection, or back to an opposite direction.

FIG. 15 illustrates an example optical device 1500, including acombination of transmissive and reflective diffractive gratings for tworespective colors and corresponding reflective layers, for individuallydiffracting the two colors of light. The optical device 1500 can includea first diffractive component 1510 having a first diffractive grating1512 for blue color and a second diffractive component 1520 having asecond diffractive grating 1522 for green color. Each of the first andsecond diffractive gratings 1512, 1522 can be a holographic grating,e.g., a Bragg grating or a volume grating. However, the firstdiffractive grating 1512 for the blue color is configured to be atransmissive grating that diffracts light of blue color forward withrespect to the light of blue color incident on the grating 1512, whilethe second diffractive grating 1522 for the green color is configured tobe a reflective grating that reflects light of green color backward withrespect to the light of green color incident on the grating 1522. Eachof the first and second diffractive gratings 1512 and 1522 can beindependently recorded and fixed in a recording medium, e.g., aphotosensitive material such as a photopolymer.

The first diffractive component 1510 and the second diffractivecomponent 1520 can be stacked together on a field grating substrate 1502along a direction, e.g., the Z direction. The field grating substrate1502 can be an optically transparent substrate, e.g., a glass substrate.The optically diffractive device 1500 can be in front of a display suchas LCOS, e.g., the display 594 of FIG. 5H, 594A of FIG. 5I, 594B of FIG.5J, or 594C of FIG. 5K. For example, the optically diffractive device1500 can be arranged on a cover glass 1530 of the display through anintermediately layer or spaced by a gap, e.g., an air gap.

Similar to the first and second diffractive components 1110, 1120 inFIG. 11, each of the first and second diffractive components 1510 and1520 can include a respective substrate 1514, 1524 and a respectivecarrier film 1516, 1526 on opposite sides of the respective diffractivegrating 1512, 1522. The respective diffractive grating 1512, 1522 isbetween the respective substrate 1514, 1524 and the respective carrierfilm 1516, 1526. The respective substrate 1514, 1524 can be a glasssubstrate that can have a refractive index same as or close to therefractive index of the field grating substrate 1502. The respectivecarrier film 1516, 1526 can be a TAC film. The TAC film can have a lowerrefractive index than a photosensitive polymer used to recorddiffractive gratings 1512 and 1522. Adjacent layers or components in theoptically diffractive device 1500 can be attached together using one ormore intermediate layers of OCA, UV-cured or heat-cured optical glues,optical contacting, or index matching fluid. For example, the firstdiffractive component 1510 (e.g., the substrate 1514) can be attached tothe field grating substrate 1502 through an intermediate layer 1501,e.g., an OCA layer. The first and second diffractive components 1510 and1520, e.g., the carrier film 1516 and the substrate 1524, can beattached together through another intermediate layer 1503, e.g., an OCAlayer. The optically diffractive device 1500 (e.g., the carrier film1526) can be attached to the cover glass 1530 of the display through anintermediate layer 1505, e.g., an OCA layer.

As shown in FIG. 15, the first diffractive grating 1512 is configured todiffract a blue color of light incident at a first incident angle θ_(b),e.g., 78.4°, into first order at a respective diffracted angle, e.g.,normal to the display, and zero order at the respective incident angle,and transmit a green color of light at a different incident angle, e.g.,due to Bragg selectivity. Thus, there can be no crosstalk between thedifferent colors of light individually diffracted at correspondingdiffractive gratings. Each color of light can be polarized. Thepolarization state of the different colors of light diffracted at firstorder can be the same, e.g., s or p.

The optically diffractive device 1500 can include a first reflectivelayer (or blocking layer) between the first grating 1512 and the secondgrating 1522. The first grating 1512 is configured to diffract the bluecolor of light incident at the first incident angle θ_(b), e.g., 78.4°,into first order at a diffracted angle, e.g., 0° and zero order at thefirst incident angle. The first reflective layer, e.g., a refractiveindex of the first reflective layer, is configured to totally reflectthe blue color of light diffracted at the first incident angle but totransmit the green color of light incident at a second incident angle.For example, the refractive index of the first reflective layer is lowerthan the refractive index of a layer immediately before the firstreflective layer, e.g., the first grating 1512. The first reflectivelayer can be a suitable layer between the first grating 1512 and thesecond grating 1522. In some examples, the first reflective layer is thecarrier film 1516, as shown in FIG. 15.

The optically diffractive device 1500 can include a second reflectivelayer after the second grating 1512 and before the display cover glass1530. The second reflective layer can be the intermediate layer 1505 andbe configured to reflect, e.g., totally, the green color of light backto the second grating 1512. The second grating 1512 is then configuredto diffract the green color of light incident at the second incidentangle θ_(g), e.g., 76.5°, into first order at a diffracted angle, e.g.,0°, back towards the display and zero order at the second incident angleback into the optically diffractive device 1500.

The totally reflected blue color of light by the reflective layer 1516and the zero order transmitted green color of light are back into theoptically diffractive device 1500 to a side of the optically diffractivedevice 1500. As illustrated in FIG. 15, a surface of the side can becoated with an optical absorber 1504, e.g., a black coating, to absorbthe blue and green colors of light at zero order by the correspondingtransmissive and reflective diffractive gratings 1512 and 1522.

Each of optically diffractive devices with color-selective polarizers(e.g., as illustrated in FIGS. 9A to 10B) and optically diffractivedevices with reflective layers (e.g., as illustrated in FIGS. 11 to 12Cand 15) can be considered as a one-dimensional beam expander. Theone-dimensional beam expander can be configured to expand an input beamwith a width and a height into an output beam with either the same widthand a greater height or the same height and a greater width, e.g., bydiffracting the input beam at one or more diffracted angles.

The techniques described herein can also be used to expand an input beaminto an output beam which is both wider and higher than the input beam,e.g., with a two-dimensional beam expansion. The two-dimensional beamexpansion can be achieved by using a two-dimensional beam expander (or adual beam expander) having at least two one-dimensional beam expandersin series. For example, a first one-dimensional beam expander can beconfigured to expand an input beam in a first dimension, either width orheight, producing an intermediate beam which is wider or higher than theinput beam in the first dimension. A second one-dimensional beamexpander can be configured to expand the intermediate beam in a seconddimension, either height or width, to produce an output beam which ishigher or wider than the intermediate beam in the second dimension.Thus, the output beam can be both wider and higher than the input beamin the first dimension and the second dimension.

In such a two-dimensional beam expander configuration, either one orboth of the one-dimensional beam expanders can use the color-selectivetechnique, and either one or both of the one-dimensional beam expanderscan use the reflective layers technique. Each one-dimensional expandercan use any of the detailed embodiments herein including reflective orrefractive diffractive elements or a combination of reflective andrefractive diffractive elements. The one-dimensional beam expanders canbe positioned in a sequential order in any suitable arrangements orconfigurations.

In some implementations, the intermediate beam between two suchone-dimensional expanders can be coupled from the first one-dimensionalexpander into the second one-dimensional expander using a free-spacein-air geometry or through a monolithic or segmented substrate made, forexample, of glass or acrylic, and embodying the geometry andfunctionality of the substrates of both expanders. This coupling can beachieved using one or more coupling elements between the twoone-dimensional expanders. The coupling elements can include a mirror,mirrors, or a mirror and a beam-splitting dichroic component, orthin-film elements of further diffractive elements. The couplingelements can take collinear collimated output light of two or morecolors from the first one-dimensional expander and convert the collinearcollimated output light of the two or more colors to two or moreindependent collimated but not collinear intermediate beams, each forone of the colors, to satisfy the color-dependent angular inputrequirements, if any, of the second one-dimensional expander. Similarly,the first one-dimensional expander can have as its input eithercollinear collimated outputs of two or more light sources (e.g., laserdiodes), each with a different color, or can have as its inputs two ormore independent collimated but not collinear intermediate beams, eachfor one color from two or more light sources.

Display Zero Order Light Suppression

A display (e.g., LCoS) includes an array of display elements (e.g.,pixels or phasels). There are gaps between the display elements on thedisplay. The gaps occupy part of an area of the display, e.g., in arange from 5% to 10%. The gaps can be considered as dead gaps becausedisplay materials (e.g., liquid crystal) at these gaps are notcontrolled by an input control signal and thus no holographicinformation can be input into these gaps. In contrast, holographicinformation can be input into the display elements that are controlled(or modulated) to diffract light to reconstruct a holographic scenecorresponding to the holographic information.

FIG. 16 illustrates an example 1600 of incident light 1620 incident on adisplay 1610. The display 1610 can be the display 114 of FIG. 1A, thedisplay 156 of FIG. 1B, the display 512 of FIG. 5A, the display 524 ofFIG. 5B, the display 534 of FIG. 5C, the display 544 of FIG. 5D, thedisplay 564 of FIG. 5E, the display 574 of FIG. 5F, the display 584 ofFIG. 5G, the display 594 of FIG. 5H, the display 594A of FIG. 5I, thedisplay 594B of FIG. 5J, the display 594C of FIG. 5K, the display 600 ofFIG. 6A, or the display 650 of FIG. 6B. Other display arrangements arealso possible.

As an example, the display 1610 can be an LCoS made of liquid crystal.The display 1610 includes an array of display elements 1612 (e.g., thedisplay element 160 of FIG. 1B) that are spaced apart by gaps 1614. Eachdisplay element 1612 can have a square (or rectangular or any othersuitable) shape that has an element width 1613, e.g., 5 μm. The displayelement 1612 can also be any other suitable shape, e.g., polygon.Adjacent display elements 1612 is separated by a gap 1614 with a gapsize 1615, e.g., less than 0.5 μm.

The incident light 1620 can be a collimated light beam that can have abeam size larger than an entire area of the display 1610, such that theincident light 1620 can illuminate the entire area of the display 1610.When the incident light 1620 is incident on the display 1610 at anincident angle θ_(i), a first portion of the incident light 1620 (e.g.,90% to 95% of the light 1620) illuminates the display elements 1612 anda second portion of the incident light 1620 (e.g., 5% to 10% of thelight 1620) illuminates the gaps 1614. When the display elements 1612are modulated with holographic information (e.g., a hologramcorresponding to holographic data), e.g., by voltages, the first portionof the incident light 1620 can be diffracted by the modulated displayelements 1612 at first order with a diffraction angle θ_(d) to becomediffracted first order light 1622.

The diffracted first order light 1622 forms a holographic light fieldthat can be a reconstruction cone (or frustum) 1630 with a viewing angleθ_(a). The viewing angle θ_(a) is dependent on one or morecharacteristics of the display 1610 (e.g., the element pitch 1613) andone or more wavelengths of the incident light 1620. In some examples, ahalf of the viewing angle θ_(a) is within a range from 3° to 10°, e.g.,5°. For example, for the pitch d=3.7 μm, the viewing angle θ_(a) isabout 7° in air for blue color of light (λ=460 nm) and about 10° in airfor red color of light at (λ=640 nm). Light with a larger wavelengthcorresponds to a larger viewing angle.

As the gaps 1614 of the display 1610 are not modulated by anyholographic information, the display 1610 at the gaps 1614 acts like areflective mirror. When the second portion of the incident light 1620 isincident on the gaps 1614, the second portion of the incident light 1620can be reflected at the gaps 1614 with a reflected angle θ_(r) that hasan absolute value identical to that of the incident angle θ_(i). In thepresent disclosure herein, “A is identical to B” indicates that anabsolute value of A is identical to that of B, and A's direction can beeither the same or different from B's direction. The reflected secondportion of the incident light 1620 can be considered as at least a partof display zero order light 1624. If the incident angle θ_(i) is lessthan the half of the apex angle θ_(a), e.g., θ_(i)=0°, the display zeroorder light 1624 may undesirably appear in the reconstruction cone,which can affect an effect of the holographic scene.

The display zero order light can also include any other unwanted lightfrom the display, e.g., diffracted light at the gaps, reflected lightfrom the display elements, or reflected light from a display cover onthe display. Higher orders of the display zero order light 1624 caninclude the diffracted light at the gaps. In some implementations, thedisplay 1610 is configured to suppress the higher orders of the displayzero order light, e.g., by including irregular or non-uniform displayelements that have different sizes. The display elements can have noperiodicity, and can form a Voronoi pattern, e.g., as illustrated inFIG. 6A.

In the present disclosure herein, for illustration purposes only,reflected second portion of the incident light is considered as arepresentative of display zero order light.

FIGS. 17A-17B illustrate examples 1700, 1750 of display zero order lightwithin a holographic scene displayed on a projection screen (FIG. 17A)and on a viewer's eye (FIG. 17B). Collimated input light 1720 is coupledby an optical device 1710 to illuminate the display 1610 at normalincidence, i.e., θ_(i)=0°. The optical device 1710 can be a waveguide, abeam splitter, or an optically diffractive device. For illustration, theoptical device 1710 is an optically diffractive device, e.g., the device598 of FIG. 5H, that includes a grating 1714 formed on a substrate 1712.However, as noted above, reflective optical devices may be used.

A first portion of the input light 1720 is incident on the displayelements 1612 of the display 1610 that are modulated with holographicinformation, and is diffracted by the display elements 1612 to becomediffracted first order light 1722. A second portion of the input light1720 is incident on the gaps 1614 of the display 1610, and is reflectedat the gaps 1614 to become at least a part of display zero order light1724. The diffracted first order light 1722 propagates in space to forma reconstruction cone with a viewing angle, e.g., 10°. As the incidentangle, e.g., 0°, is less than a half of the viewing angle, e.g., 5°, thedisplay zero order light 1724 propagating with a reflected angleidentical to the incident angle, e.g., 0°, is within the reconstructioncone.

As illustrated in FIG. 17A, the diffracted first order light 1722 formsa three-dimensional holographic scene, a two-dimensional cross-section1732 of which may be observed on a two-dimensional (2D) projectionscreen 1730 that is spaced away from the display 1610 along a directionperpendicular to the display 1610. The display zero order light 1724appears to be collimated zero order light 1734 as an undesired image(e.g., having a rectangular shape) within the holographic scene 1732. Asillustrated in FIG. 17B, the diffracted first order light 1722 forms aholographic scene 1762 on an eye of a viewer 1760. The display zeroorder light 1724 is focused by a lens of the eye of the viewer 1760 andappears to be focused zero order light 1764 as an undesired spot withinthe holographic scene 1762.

To improve an effect of a reconstructed holographic scene and thus aperformance of a display system, it is desirable to suppress (or eveneliminate) display zero order light in the reconstructed holographicscene. Implementations of the present disclosure provide multipletechniques, e.g., five techniques as described below, to suppress (oreven eliminate) the display zero order light in the reconstructedholographic scene. The techniques can be applied individually or in acombination thereof.

The display zero order light can be suppressed in the reconstructedholographic scene with a light suppression efficiency. The lightsuppression efficiency is defined as one minus a ratio between an amountof the display zero order light in the holographic scene with thesuppression using the technique described herein and an amount ofdisplay zero order light in the holographic scene without suppression.In some examples, the light suppression efficiency is more than apredetermined percentage, e.g., 50%, 60%, 70%, 80%, 90%, or 99%. In someexamples, the light suppression efficiency is 100%. That is, all thedisplay zero order light is eliminated in the holographic scene.

In a first technique referred to as “phase calibration,” phases ofdisplay elements of a display can be adjusted to have a predeterminedphase range, e.g., [0, 2π]. In such a way, a signal to noise ratio (S/N)between a holographic scene formed based on the calibrated phases anddisplay zero order light can be increased.

In a second technique referred to as “zero order beam divergence,” asillustrated in FIG. 18, a display zero order light beam is diverged byan optically defocusing device (e.g., a concave lens) to have a lowerpower density. In contrast, a hologram is preconfigured, such thatcollimated light beam incident on display elements modulated by thehologram is diffracted to become a converged light beam. The convergedlight beam is re-focused by the optically defocusing device to form aholographic scene with a higher power density. Thus, the display zeroorder light beam is diluted or suppressed in the holographic scene.

In a third technique referred to as “zero order light deviation,” asillustrated in FIGS. 19A-19C, 20A-20B, 21, and 22, display zero orderlight is deviated away from a holographic scene. An optical device isconfigured to couple input light to illuminate a display at an incidentangle larger than a half of a viewing angle of a reconstructed cone thatforms the holographic scene. The display zero order light propagatesaway from the display at a reflected angle identical to the incidentangle. A hologram corresponding to the holographic scene ispreconfigured such that diffracted first order light propagates awayfrom the display to form the reconstruction cone in a same way as thatwhen the incident angle is 0°. Thus, the display zero order light isdeviated from the reconstruction cone and accordingly the holographicscene.

In a fourth technique referred to as “zero order light blocking,” asillustrated in FIGS. 23A-23B, display zero order light is first deviatedaway from diffracted first order light according to the third techniqueand then blocked (or absorbed) by an optically blocking component, e.g.,a metamaterial layer or an anisotropic optical element such as a louverfilm. The optically blocking component is configured to transmit a lightbeam having an angle smaller than a predetermined angle and block alight beam having an angle larger than the predetermined angle. Thepredetermined angle can be smaller than the incident angle of the inputlight and larger than a half of the viewing angle of the reconstructioncone.

In a fifth technique referred to as “zero order light redirection,” asillustrated in FIGS. 24 to 33, display zero order light is firstdeviated away from diffracted first order light according to the thirdtechnique and then redirected even further away from the diffractedfirst order light by an optically diffractive component, e.g., adiffractive grating. When the input light includes different colors oflight simultaneously or sequentially, as illustrated in FIGS. 30A-30B,31A-31B, 32, and 33, the optically diffractive component can include oneor more corresponding diffractive gratings that are configured todiffract the different colors of light towards different directions in aplane or in space to reduce color crosstalk among the different colorsof light.

The above five techniques are mainly used to suppress main reflectedzero order of the whole display zero order light. In a sixth technique,the display is configured to suppress higher orders of the whole displayzero order light, e.g., by using irregular or nonuniform displayelements having different sizes or shapes or both. The display elementscan have no periodicity, and can form a Voronoi pattern or be Voronoilpatterned display elements. In some implementations, the display can bethe display 600 of FIG. 6A or the display 650 of FIG. 6B.

In the following, the first five techniques are described with moredetails.

First technique—Phase Calibration

Phase calibration is a technique that can increase a contrast in adisplay, e.g., by pulling a direct current (DC) term of a computedhologram out, which can be implemented by a software or programinstructions. Phase calibration can achieve an accuracy beyond a devicecalibration that may be bad or unknown.

In some implementations, a hologram includes respective phases fordisplay elements of a display. As described above, the respective phasecan be a computed EM contribution from one or more corresponding objectsto each display element. According to the phase calibration technique,the hologram is configured by adjusting (e.g., scaling and/or shifting)the respective phases for the display elements to have a predeterminedphase range, e.g., [0, 2π], to get a higher contrast in the display.

The respective phases can be adjusted according to an expression:

Ø_(a) =AØ _(i) +B  (15),

where θ_(i) represents an initial phase value of a respective phase,θ_(a) represents an adjusted phase value of the respective phase, and Aand B are constants for the respective phases, A being in [0, 1] and Bbeing in [0, 2π]. In some examples, A is the same for all displayelements. In some examples, B is the same for all display elements. Insome examples, A is different for different display elements. In someexamples, B is different for different display elements.

In a perfectly calibrated and linearized display system, a pair ofvalues (1, 0) for (A, B) works best to give the best contrast by provingthe highest diffraction efficiency for the input hologram. However, dueto nonlinear LC curves and inaccurate calibration of the display, therespective phases for the display elements are typically not in a rangeof [0, 2π], and thus the display contrast is degraded. As the inputlight is the same, the display zero order light will be the same. If thediffraction efficiency of the hologram is increased, the displaycontrast can be higher and the S/N ratio of the holographic scene can behigher.

According to the phase calibration technique, the display contrast canbe improved by scaling and shifting the respective phases in a phasecoordinate system, such that the respective phases are adjusted to havea range, e.g., exactly [0, 2π]. In some cases, the range of the adjustedrespective phases can be smaller or larger than the 2π range dependingon the calibration and the maximum phase shift of the working LC.Therefore, for each display, there can be a pair of (A, B) that producesthe highest diffraction efficiency resulting in the highest S/N ratio.

The respective phases for the display elements can be adjusted byadjusting the constants A and B such that a light suppression efficiencyfor the holographic scene is maximized. The light suppression efficiencycan be larger than a predetermined percentage, e.g., 50%, 60%, 70%, 80%,90%, or 99%.

In some implementations, the constants A and B are adjusted by a machinevision algorithm or a machine learning algorithm such as an artificialintelligence (AI) algorithm. In the machine vision algorithm, a hologramis designed to create pseudo-random points focused on a transmissivediffusing screen in a plane at a specific distance from the display.Then, the hologram is computed for each of three primary colors red,green, and blue (RGB) in a way that the RGB reconstructed points arealigned perfectly on that plane. Then the algorithm is set to find apair of values (A, B) for each color so that a display contrast is at anacceptable level. At the beginning for a pair of values (A, B), e.g.,[1, 0], a camera at the specific distance takes a picture of the patternon the screen. In the taken picture, a brightness of all the points (X)is averaged, and also one small area (Y) on a background noise ismeasured. The ratio of X/Y is calculated and checked if it is largerthan a specific value. If not, the pair of values (A, B) will be changedand the process is automatically repeated until an acceptable pair ofvalues (A, B) is determined.

Second technique—Zero Order Beam Divergence

FIG. 18 illustrates an example system 1800 of suppressing display zeroorder light in a holographic scene displayed on a projection screen 1830by diverging the display zero order light beam. A beam splitter 1810 ispositioned in front of a display 1610 and couples a collimated inputlight beam 1820 to illuminate the display 1610 at normal incidence. Afirst portion of the light beam 1820 is diffracted by display elementsmodulated by a hologram to become a diffracted first order light beam1822, and a second portion of the light beam 1820 is reflected by gapsof the display 1610 to become a display zero order light beam 1824. Anoptically diverging component, e.g., a concave lens 1802, is arrangeddownstream the beam splitter 1810 and before the projection screen 1830.In some examples, the optically diverging component includes a convexlens arranged at a position further away from the projection screen 1830than the concave lens 1802 such that a collimated light beam is firstfocused and then diverged towards the projection screen 1830.

When the display zero order light beam 1824 comes off the display 1610,the display zero order light beam 1824 is collimated. Thus, when thedisplay zero order light beam 1824 transmits through the concave lens1802, the display zero order light beam 1824 is diverged by the concavelens 1802, as illustrated in FIG. 18. Thus, a power density of thediverged display zero order light beam 1824 is decreased or diluted overthe diverged beam area, compared to that of the original collimatedinput light beam 1820.

According to the second technique, the hologram (or respective phases)modulating display elements of the display 1610 can be preconfiguredsuch that the diffracted first order light beam 1822 is converged whencoming off the display 1610. The degree of convergence is configured tocorrespond to a degree of divergence of the concave lens 1802. That is,the divergence of the concave lens is compensated by the configuredconvergence. Thus, when the converged diffracted first order light beam1822 transmits through the concave lens 1802, the diffracted first orderlight beam 1822 is collimated to form a reconstructed holographic scene1832 on a projection screen 1830, which is the same as that without thepre-configuration of the hologram and the concave lens 1802. Thus, thereconstructed holographic scene 1832 has a power density the same asthat of the collimated input light beam 1820. In contrast, a displayzero order light beam 1834 is diverged and smeared (or diluted) acrossthe projection screen 1830 with a decreased power density. Theprojection screen 1830 is spaced away from the display 1610 with aspecified distance, e.g., 50 cm. The display zero order light beam 1834can be dim and appear like a background noise in the holographic scene1832. In such a way, a light suppression efficiency can be increased,e.g., to more than 99%, and an S/N ratio of the holographic scene 1832can be increased.

In some implementations, the hologram is preconfigured by addingcorresponding phases to the respective phases for the display elementsof the display 1610. The respective phases for the display elements canbe the respective phases adjusted according to the first technique—phasecalibration. The corresponding phase for each of the display elements isexpressed as:

$\begin{matrix}{{\varnothing = {\frac{\pi}{\lambda f}\left( {{ax^{2}} + {by^{2}}} \right)}},} & (16)\end{matrix}$

where Ø represents the corresponding phase for the display element, λrepresents a wavelength of the input light 1820, f represents a focallength of the optically diverging component (e.g., the concave lens1802), x and y represent coordinates of the display element in a 2Ddisplay coordinate system, and a and b represent constants. A pair ofvalues (a, b) can be adjusted based on applications, e.g., forintroducing astigmatism for people whose eyes suffer from astigmatism.If a is identical to b, e.g., a=1 and b=1, a defocusing effect of thecorresponding phase is circular; if a is different from b, e.g., a=1 andb=0.5, the defocusing effect is elliptical and can match a 2:1anamorphic focusing lens. If either a=0 or b=0, but not both, thedefocusing effect can produce a line focus rather than an area focus andcan match a cylindrical focusing lens.

In some implementations, the hologram is preconfigured by adding avirtual lens for a configuration cone when designing (or simulating) theholographic scene in a 3D software application such as Unity, e.g., theapplication 106 of FIG. 1A. The configuration cone is described withfurther details in FIGS. 20A-20B. The diffracted first order light beam1822 forms a reconstruction cone with a viewing angle, and theconfiguration cone corresponds to the reconstruction cone and has anapex angle identical to the viewing angle. In the simulation, theconfiguration cone can be moved with respect to the display in a global3D coordinate system along a direction perpendicular to the display witha distance corresponding to a focal length of the optically divergingcomponent. The configuration cone can be moved just once for all objectsin the reconstruction cone. Holographic data, e.g., primitive lists forthe objects, are then generated based on the moved configuration cone inthe global 3D coordinate system.

Third technique—Zero Order Light Deviation

As described above in FIGS. 16 and 17A-17B, a reconstruction cone of aholographic scene (or holographic content) has a viewing angle dependingon a display and a wavelength of an input light beam. If display zeroorder light can be deviated outside of the reconstruction cone, theholographic scene can be observed without the display zero order light.

FIG. 19A illustrates an example system 1900 of display zero order lightin a holographic scene when a display 1610 is illuminated withcollimated input light 1920 at normal incidence, i.e., θ_(i)=0°. Anoptical device 1910 couples the collimated input light 1920 toilluminate the display 1610 at the normal incidence. In someimplementations, as illustrated in FIG. 19A, the optical device 1910 isa waveguide device, e.g., the waveguide device 588 of FIG. 5G, thatincludes an incoupler 1916 and an outcoupler 1914 formed on a substrate1912.

A first portion of the input light 1920 is incident on display elementsof the display 1610 that are modulated with a hologram, and isdiffracted by the display elements to become diffracted first orderlight 1922. A second portion of the input light 1920 is incident on gapsof the display 1610, and is reflected at the gaps to become at least apart of display zero order light 1924. The diffracted first order light1922 propagates in space to form a reconstruction cone with a viewingangle, e.g., 10°. As the incident angle, e.g., 0°, is less than a halfof the viewing angle, e.g., 5°, the display zero order light 1924propagating with a reflected angle identical to the incident angle,e.g., 0°, is within the reconstruction cone. As illustrated in FIG. 19A,the diffracted first order light 1922 forms a holographic scene 1932 ona two-dimensional (2D) projection screen 1930. The display zero orderlight 1924 appears to be collimated zero order light 1934 as anundesired image within the holographic scene 1932.

FIG. 19B illustrates an example 1950 of suppressing display zero orderlight in a holographic scene displayed on the projection screen 1930 bydirecting (or deviating) display zero order light away from theholographic scene. Different from the optical device 1910, an opticaldevice 1960, including incoupler 1966 and outcoupler 1964 formed on asubstrate 1962, is configured to couple the collimated input light 1920to illuminate the display 1610 at an incident angle θ_(i) larger than0°. Due to reflection, display zero order light 1974 comes off thedisplay 1610 at a reflected angle θ_(r) identical to the incident angleθ_(i).

According to the third technique, a hologram (or respective phases)modulating display elements of the display 1610 can be preconfiguredsuch that diffracted first order light 1972 comes off the display 1610at normal incidence. That is, the deviation of the incident angle iscompensated by the configured hologram. Thus, the diffracted first orderlight beam 1972 forms a reconstruction cone that appears as areconstructed holographic scene 1976 on the projection screen 1930, thesame as when the incident angle is at normal incidence. When theincident angle, e.g., 6°, is larger than a half of the viewing angle ofthe reconstruction cone, e.g., 5°, the display zero order light 1974 canbe deviated or shifted away from the reconstruction cone. Accordingly,as illustrated in FIG. 19B, a shifted display zero order image 1978formed by the display zero order light 1974 can be outside of theholographic scene 1976 on the projection screen 1930. Similarly, asillustrated in FIG. 19C, when seen by a viewer 1990, a display zeroorder spot 1994 formed by the display zero order light 1974 can beoutside of a holographic scene 1992 formed by the diffracted first orderlight 1972 on an eye of the viewer 1990. By configuring a direction ofthe incident angle, the display zero order light can be deviated up ordown or to a side in space.

In some implementations, the hologram is preconfigured by addingcorresponding phases to the respective phases for the display elementsof the display 1610. The respective phases for the display elements canbe the respective phases adjusted according to the first technique—phasecalibration. The corresponding phase for each of the display elements isexpressed as:

$\begin{matrix}{{\varnothing = {\frac{2\pi}{\lambda}\left( {{x\;\cos\;\theta} + {y\;\cos\;\theta}} \right)}},} & (17)\end{matrix}$

where Ø represents the corresponding phase for the display element, λrepresents a wavelength of the input light 1920, x and y representcoordinates of the display element in a 2D display coordinate system (orin a 3D coordinate system), and θ represents an angle corresponding tothe incident angle θ_(i), e.g., θ=θ_(i).

In some implementations, the hologram is preconfigured by adding avirtual prism for a configuration cone when designing (or simulating)the holographic scene in a 3D software application such as Unity, e.g.,the application 106 of FIG. 1A.

FIG. 20A illustrates an example 2000 of a configuration cone 2020 and areconstruction cone 2030 with respect to a display 2002 and an opticaldevice 2010 in a 3D coordinate system in the 3D software application.The optical device 2010 can be a lightguide device, e.g., the opticallydiffractive device 598 of FIG. 5H, that includes a grating 2014 formedon a substrate 2012.

As illustrated in FIG. 20A, the optical device 2010 couples input light2040 to illuminate the display 2002 with an incident angle larger than0°, not at normal incidence, which is identical in effect to rotatingthe configuration cone 2020 (together with all objects including anobject 2022 within the configuration cone 2020) with an anglecorresponding to (e.g., identical to) a reflected angle of the incidentangle with respect to the 3D coordinate system. In some implementations,the configuration cone 2020 is rotated in the original 3D coordinatesystem. In some implementations, the original 3D coordinate system isrotated but the configuration cone 2020 is not rotated. Once theconfiguration cone 2020 in the 3D coordinate system is set, objects canbe placed in the configuration cone 2020 without changing primitives'vertices individually. Accordingly, the simulated reconstruction cone2030 (with all reconstructed objects including a reconstructed object2032) and display zero order light 2042 are rotated with respect to thedisplay 2002 with the same reflected angle with respect to the 3Dcoordinate system. That is, the display zero order light 2042 can appearin a holographic scene when seen by a viewer.

FIG. 20B illustrates an example 2050 of adjusting the configuration cone2020 of FIG. 20A to configure a hologram corresponding to theholographic scene in the 3D coordinate system in the 3D softwareapplication. The configuration cone 2020 (together with the designedobjects including the object 2022) can be rotated with a rotation anglewith respect to a surface of the display 2002 in the 3D coordinatesystem. The rotation angle is corresponding to (e.g., identical to) theincident angle so that an adjusted configuration cone 2060 (with theadjusted designed objects including the adjusted object 2062) is atnormal incidence to the display 2002. The configuration cone 2020 can beadjusted just once for all the designed objects. Holographic data, e.g.,primitive lists for the objects, are then generated based on theadjusted configuration cone 2060 in the global 3D coordinate system. Thehologram is then generated based on the holographic data.

Accordingly, when the optical device 2010 couples the input light 2040to illuminate the display 2002 at the incident angle, a first portion ofthe input light 2040 is diffracted by the display elements modulatedwith the preconfigured hologram. The diffracted first order light formsa reconstruction cone 2070 (with reconstructed objects including thereconstructed object 2072 of the designed object 2062) normal to thedisplay 2002. The reconstruction cone 2070 has a viewing angle θ, Incontrast, a second portion of the input light 2040 is reflected at thegaps without the modulation of the preconfigured hologram to becomedisplay zero order light 2042 that comes off the display at a reflectedangle θ_(r) identical to the incident angle θ_(i). Thus, when theincident angle θ_(i) is larger than a half of the viewing angle, i.e.,θ_(i)>θ_(v)/2, the display zero order light 2042 is outside thereconstruction cone 2070 and accordingly the holographic scene when seenby a viewer.

The input light 2040 can be coupled into the optical device 2010 in anysuitable way, e.g., by an incoupler such as the incoupler 1966 of FIG.19B, by a prism as illustrated in FIG. 21, or a wedged substrate asillustrated in FIG. 22.

FIG. 21 illustrates an example 2100 of coupling collimated input light2120 via a coupling prism 2111 to an optical device 2110 to illuminate adisplay 1610 at an incident angle for suppressing display zero orderlight in a holographic scene. The optical device 2110 includes a grating2114 on a substrate 2112. The coupling prism 2111 couples the inputlight 2120 into the substrate 2112 that guides the input light 2120towards the grating 2114. The grating 2114 diffracts the input light2120 out towards the display 1610 at the incident angle. A hologram ispreconfigured such that diffractive first order light 2122 comes off thedisplay 1610 surrounding normal incidence to form a reconstruction cone,while display zero order light 2124 comes off the display 1610 at areflected angle identical to the incident angle. When the incident angleis larger than a half of a viewing angle of the reconstruction cone, thedisplay zero order light 2124 forms a shifted zero order spot 2134outside of a holographic scene 2132 when seen by a viewer 2130.

FIG. 22 illustrates an example system 2200 of coupling light via awedged substrate 2212 of an optical device 2210 to illuminate a display1610 at an incident angle for suppressing display zero order light in aholographic scene. The optical device 2210 includes a grating 2214 onthe wedged substrate 2212. The wedged substrate 2212 couples the inputlight 1020 into the substrate 2212 that guides the input light 2120towards the grating 2214. The grating 2214 diffracts the input light2120 out towards the display 1610 at the incident angle. A hologram ispreconfigured such that diffractive first order light 2222 comes off thedisplay 1610 surrounding normal incidence to form a reconstruction cone,while display zero order light 2224 comes off the display 1610 at areflected angle identical to the incident angle. When the incident angleis larger than a half of a viewing angle of the reconstruction cone, thedisplay zero order light 2224 forms a shifted zero order spot 2234outside of a holographic scene 2232 when seen by a viewer 2230.

According to the third technique, the display zero order light comingoff the display has a larger deviation angle than the diffracted firstorder light coming off the display. Thus, the display zero order lightcan be suppressed (or eliminated) in the holographic scene based on theangle difference, e.g., as described further in the fourth technique“zero order light blocking” and the fifth technique “zero order lightredirection.”

Fourth technique—Zero Order Light Blocking

FIGS. 23A-23B illustrate example systems 2300, 2350 of suppressingdisplay zero order light in a holographic scene by blocking or absorbingthe display zero order light reflected from the display by an opticallyblocking component. The optically blocking component can be any suitablestructure, e.g., an artificial structure such as a louvered layer, ametamaterial layer, a metamaterial structure, a metasurface, or anyother kind of engineered microstructure or nanostructure that canexhibit the blocking property.

For illustration, similar to FIG. 21, a coupling prism 2311 couples acollimated input light 2320 into an optical device 2310 having a grating2314 formed on a substrate 2312. The grating 2314 is configured todiffract the input light 2320 out to illuminate a display 1610 at anincident angle, e.g., larger than a half of a viewing angle of areconstruction cone. By applying the third technique, a hologram ispreconfigured such that diffracted first order light 2322 comes off thedisplay 1610 in a same way as that when the input light is incident onthe display at normal incidence, while display zero order light 2324propagates away from the display 1610 at a reflected angle identical tothe incident angle.

A metamaterial layer 2316, as an example of the optically blockingcomponent, is formed on (e.g., deposited upon, or attached to) thesubstrate 2312. As illustrated in FIGS. 23A-23B, the metamaterial layer2316 and the grating 2314 can be formed on opposite sides of thesubstrate 2312. The metamaterial layer 2316 can be made of an array ofmicrostructures or nanostructures smaller than a wavelength of interest.By configuring a geometry of the microstructures or nanostructuresindividually and collectively, the metamaterial layer 2316 can bedesigned to interact with light in a desire manner. In the presentdisclosure, the metamaterial layer 2316 is configured to transmit alight beam having an angle smaller than a predetermined angle and blocka light beam having an angle larger than the predetermined angle. Thepredetermined angle can be set to be smaller than the incident angle andlarger than the half of the viewing angle of the reconstruction coneformed by the diffracted first order light 2322. Thus, the diffractedfirst order light 2322 can be transmitted through the metamaterial layer2316 with a transmission efficiency, e.g., no less than a predeterminedratio such as 50%, 60%, 70%, 80%, 90%, or 99%. In contrast, the displayzero order light can be blocked or absorbed by the metamaterial layer2316, e.g., with a blocking efficiency of 100%.

A light suppression efficiency of the display zero order light in aholographic scene can be 100%. As illustrated in FIG. 23A, thediffracted first order light 2322 can form a holographic scene 2332 on aprojection screen 2330, without the display zero order light 2324. Asillustrated in FIG. 23B, when seen by a viewer 2360, the diffractedfirst order light 2322 can form a holographic scene 2362 on an eye ofthe viewer 2360, without the display zero order light 2324.

Fifth technique—Zero Order Light Redirection

FIG. 24 illustrates a system 2400 of suppressing display zero orderlight in a holographic scene by redirecting the display zero order lightaway from the holographic scene via an optically redirecting structure.The optically redirecting structure can be a grating, e.g., aholographic grating such as a Bragg grating, or any other suitableredirecting structure.

Similar to the system 590 of FIG. 5H, the system 2400 includes acomputer 2401 (e.g., the computer 591 of FIG. 5H), a controller 2402(e.g., the controller 592 of FIG. 5H), a reflective display 2404 (e.g.,the reflective display 594 of FIG. 5H), and an illuminator 2406 (e.g.,the illuminator 596 of FIG. 5H). The system 2400 also includes anoptical device 2410 that can include an optically diffractive device,e.g., the optically diffractive device 598 of FIG. 5H, 598A of FIG. 5I,598B of FIG. 5J, or 598C of 5K, the optically diffractive device 900 ofFIGS. 9A and 9B, 1000 of FIGS. 10A and 10B, 1100 of FIG. 11, 1200 ofFIG. 12A, 1250 of FIG. 12B, or 1270 of FIG. 12C, or 1500 of FIG. 15. Insome implementations, as illustrated in FIG. 24, the optical device 2410includes a transmissive field grating structure 2414 as the opticallydiffractive device on a substrate 2412 (e.g., the substrate 598-2 ofFIG. 5H). The transmissive field grating structure 2414 can be the fieldgrating structure 598-1 of FIG. 5H. The transmissive field gratingstructure 2414 can include one or more gratings for one or moredifferent colors of light. The substrate 2412 can be a transparent glasssubstrate.

Similar to what is described above, the optical device 2410 can bearranged adjacent to a front surface of the display 2404. In someimplementations, a top surface of the optical device 2410 (e.g., asurface of the field grating structure 2414) is attached to the frontsurface of the display 2404, e.g., through an index matching material.In some implementations, an air gap is between the top surfaces of theoptical device 2410 and the display 2404. In some implementations, aspacer, e.g., glass, is inserted in the air gap between the top surfacesof the optical device 2410 and the display 2404. To better illustratelight propagation, the air gap is used as an example in FIG. 24 and thefollowing FIGS. 26A to 33.

The controller 2402 is configured to receive graphic data correspondingto one or more objects from the computer 591 (e.g., by using a 3Dsoftware application such as Unity), perform computation on the graphicdata, and generate and transmit control signals for modulation to thedisplay 2404 through a memory buffer 2403. The controller 2402 is alsocoupled to the illuminator 2406 and configured to provide a timingsignal 2405 to activate the illuminator 2406 to provide input light2420. The input light 2420 is then diffracted by the transmissive fieldgrating 2414 of the optical device 2410 to illuminate the display 2404.A first portion of the input light 2420 incident on display elements ofthe display 2404 is diffracted by the display 2404, and diffracted firstorder light 2421 forms a holographic light field 2422 towards a viewer.The holographic light field 2422 can correspond to a reconstruction cone(or frustum) that has a viewing angle. The display 2404 can include aback mirror on a back of the display 2404 and can reflect light towardsthe viewer. A second portion of the input light 2420 incident on gaps ofthe display 2404 is reflected by the display 2404, e.g., by the backmirror, to become display zero order light 2424.

As described above, the transmissive field grating 2414 can beconfigured to diffract the input light 2420 from the illuminator 2406out to illuminate the display 2404 off axis at an incident angle, e.g.,larger than a half of a viewing angle of the reconstruction cone (orfrustum). By applying the third technique, the diffracted first orderlight 2421 comes off the display 2404 in the same manner as that whenthe input light 2420 is incident on axis at normal incidence, while thedisplay zero order light 2424 comes off at a reflected angle that isidentical to the incident angle, which is outside of the reconstructioncone.

As illustrated in FIG. 24, the system 2400 can include an opticallyredirecting structure 2416 configured to diffract a first light beamhaving an angle identical to a predetermined angle with a substantiallylarger diffraction efficiency at a diffraction angle than a second lightbeam having an angle different from the predetermined angle. Theoptically redirecting structure 2416 can be a holographic grating suchas a Bragg grating. The diffraction angle can be substantially largerthan the predetermined angle. In some implementations, the opticallyredirecting structure 2416 includes one or more gratings for one or moredifferent colors of light, as illustrated further in FIGS. 30A-33. Insome implementations, the optically redirecting structure 2416 isarranged downstream the optical device 2410 away from the display 2404.In some implementations, as illustrated in FIG. 24, the opticallyredirecting structure 2416 is formed on a side of the substrate 2412that is opposite to the transmissive field grating structure 2414.

According to the fifth technique, the optically redirecting structure2416 can be configured to have the predetermined angle identical to thereflected angle of the display zero order light 2424 or the incidentangle of the input light 2420 at the display 2404. As the display zeroorder light 2424 propagates at the reflected angle, the opticallyredirecting structure 2416 can diffract the display zero order light2424 with a substantially larger diffraction efficiency at thediffraction angle than the diffracted first order light 2421, while thediffracted first order light 2421 can transmit through the opticallyredirecting structure 2416 to form the holographic light field 2422. Insuch a way, the optically redirecting structure 2416 can redirect thedisplay zero order light 2424 further away from the holographic lightfield 2422.

FIGS. 25A-25C illustrate examples of redirecting display zero orderlight via zero order redirection gratings 2500, 2530, 2550 in FIGS. 25A,25B, 25C to different directions in space. The zero order redirectiongrating 2500, 2530, 2550 can be in the optically redirection gratingstructure 2416 of FIG. 24. The redirection gratings 2500, 2530, 2550 canbe fabricated according to the method illustrated in FIG. 7A.

For comparison, display zero order light 2502 is incident on the zeroorder redirection grating 2500, 2530, 2550 at an incident angle −6.0°,which is a predetermined angle for the redirection grating 2500, 2530,2550. The redirection grating 2500, 2530, 2550 is configured to diffractthe display zero order light 2502 with a high diffraction efficiency ata diffraction angle that is substantially larger than the incident angleof the display zero order light 2502. The redirection gratings 2500,2530, 2550 can be configured to diffract the display zero order light2502 at different diffraction angles, for example, 60° for the grating2500 shown in FIG. 25A, 56° for the grating 2530 shown in FIG. 25B, and−56° for the grating 2550 in FIG. 25C.

FIGS. 26A-26E illustrate examples of redirecting display zero orderlight when light is input at different incident angles via opticallyredirecting structures (e.g., zero order redirection gratings) todifferent directions in space. Each of the incident angles, e.g., −6° or6° in air, is configured to be larger than a half of a viewing angle ofa reconstruction cone corresponding to a holographic light field, e.g.,5° in air.

As illustrated in FIG. 26A, a system 2600 includes an optical device2610 that can be the optical device 2410 of FIG. 24. The optical device2610 includes a substrate 2612 (e.g., the substrate 2412 of FIG. 24), atransmissive field grating structure 2614 (e.g., the transmissive fieldgrating structure 2414 of FIG. 24), and a zero order redirection gratingstructure 2616 (e.g., the zero order redirection grating structure 2416of FIG. 24). The optical device 2610 can include a cover glass 2618 onthe zero order redirection grating structure 2616.

Input light 2620 from the illuminator 2406 is diffracted by thetransmissive field grating structure 2614 to illuminate the display 2404with an incident angle −6° (in air). A first portion of the input light2620 illuminating on modulated display elements of the display 2404 isdiffracted to transmit through the optical device 2610 (including thezero order redirection grating structure 2616) to become diffractedfirst order light 2621 that forms a holographic light field 2622. Asecond portion of the input light 2620 illuminating on gaps of thedisplay 2404 is reflected to come off the display 2404 as display zeroorder light 2624. The display zero order light 2624 is redirected by thezero order redirection grating structure 2616 at a diffraction anglesubstantially larger than the incident angle, e.g., −28° in glass. Dueto Fresnel reflection, part of the redirected display zero order lightis reflected back by an interface between the cover glass 2618 and theair to the optical device 2610, and the reflected display zero orderlight, e.g., Fresnel reflection of zero order light 2625, can beabsorbed by an optical absorber 2619 formed on an edge of the opticaldevice 2610. The optical absorber 2619 can be similar to the opticalabsorber 1104 of FIG. 11, 1204 of FIG. 12A, 12C, or 1254 of FIG. 12B.Another part of the redirected display zero order light is transmittedthrough the interface into the air downwards at a redirection angle of−45°, e.g., redirected zero order light 2626, which is far away from theholographic light field 2622.

As illustrated in FIG. 26B, a system 2630 includes an optical device2640 that can be the optical device 2410 of FIG. 24. The optical device2640 includes a substrate 2642 (e.g., the substrate 2412 of FIG. 24), atransmissive field grating structure 2644 (e.g., the transmissive fieldgrating structure 2414 of FIG. 24), and a zero order redirection gratingstructure 2646 (e.g., the zero order redirection grating structure 2416of FIG. 24). The optical device 2640 can include a cover glass 2648 onthe zero order redirection grating structure 2646.

Different from the transmissive field grating structure 2614 of theoptical device 2610 of FIG. 26A, the transmissive field gratingstructure 2644 of the optical device 2640 diffracts the input light 2620from the illuminator 2406 to illuminate the display 2404 with anincident angle +6° (in air). A first portion of the input light 2620illuminating on modulated display elements of the display 2404 isdiffracted to transmit through the optical device 2640 (including thezero order redirection grating structure 2646) to become diffractedfirst order light 2631 that forms a holographic light field 2632. Asecond portion of the input light 2620 illuminating on gaps of thedisplay 2404 is reflected to come off the display 2404 as display zeroorder light 2634. Different from the zero order redirection gratingstructure 2616 of FIG. 26A, the zero order redirection grating structure2646 redirects (or diffracts) the display zero order light 2624 at adiffraction angle substantially larger than the incident angle, e.g.,+28° in glass. Due to Fresnel reflection, part of the redirected displayzero order light is reflected back by an interface between the coverglass 2618 and the air to the optical device 2610, and the reflecteddisplay zero order light, e.g., Fresnel reflection of zero order light2635, can be absorbed by an optical absorber 2649 formed on an edge ofthe optical device 2640. The optical absorber 2649 can be similar to theoptical absorber 2619 of FIG. 26A. Another part of the redirecteddisplay zero order light is transmitted through the interface into theair upwards at a redirection angle of +45°, e.g., redirected zero orderlight 2636, which is far away from the holographic light field 2622.

As illustrated in FIG. 26C, a system 2650 includes an optical device2660 that can be the optical device 2410 of FIG. 24. The optical device2660 includes a substrate 2662 (e.g., the substrate 2412 of FIG. 24), atransmissive field grating structure 2664 (e.g., the transmissive fieldgrating structure 2414 of FIG. 24), and a zero order redirection gratingstructure 2666 (e.g., the zero order redirection grating structure 2416of FIG. 24). The optical device 2660 can include a cover glass 2668 onthe zero order redirection grating structure 2666.

Same as the transmissive field grating structure 2614 of the opticaldevice 2610 of FIG. 26A, the transmissive field grating structure 2664of the optical device 2660 diffracts the input light 2620 from theilluminator 2406 to illuminate the display 2404 with an incident angle−6° (in air). A first portion of the input light 2620 illuminating onmodulated display elements of the display 2404 is diffracted to transmitthrough the optical device 2660 (including the zero order redirectiongrating structure 2666) to become diffracted first order light 2631 thatforms a holographic light field 2632. A second portion of the inputlight 2620 illuminating on gaps of the display 2404 is reflected to comeoff the display 2404 to become at least a part of display zero orderlight 2654. Different from the zero order redirection grating structure2616 of FIG. 26A, the zero order redirection grating structure 2666redirects (or diffracts) the display zero order light 2654 at adiffraction angle substantially larger than the incident angle, e.g.,+28° in glass. Due to Fresnel reflection, part of the redirected displayzero order light is reflected back by an interface between the coverglass 2668 and the air to the optical device 2660, and the reflecteddisplay zero order light, e.g., Fresnel reflection of zero order light2655, can be absorbed by an optical absorber 2649 formed on an edge ofthe optical device 2640. The optical absorber 2669 can be similar to theoptical absorber 2619 of FIG. 26A. Another part of the redirecteddisplay zero order light is transmitted through the interface into theair upwards at a redirection angle of +45°, e.g., redirected zero orderlight 2656, which is far away from the holographic light field 2622.

To eliminate the effect of Fresnel reflection on the redirected displayzero order light on the interface between a surface of the cover glassand the air, an anti-reflection (AR) coating can be formed on thesurface of the cover glass 2668, so that the redirected display zeroorder light can be transmitted with a high transmittance into the airbut with little or no reflection back to the optical device.

As illustrated in FIG. 26D, a system 2670 includes an optical device2680. Similar to the optical device 2660 of FIG. 26C, the optical device2680 is configured to diffract the input light 2620 to illuminate thedisplay 2404 at an incident angle −6° (in air) and redirect the displayzero order light 2654 into the air upwards at a redirection angle of+45°. However, different from the optical device 2660 of FIG. 26C, theoptical device 2680 includes an AR coating layer 2682 formed on anexternal surface of the cover glass 2668, such that the redirecteddisplay zero order light is substantially transmitted through the coverglass 2668 into the air at a redirection angle of +45°, e.g., redirectedzero order light 2672. In such a way, there is little or no Fresnelreflection of the redirected zero order light back into the opticaldevice 2680.

FIG. 26E shows another example of redirecting the display zero orderlight at an even larger redirection angle, e.g., +75° in air orapproximately +40° in glass). As illustrated in FIG. 26E, a system 2690includes an optical device 2692. Similar to the optical device 2660 ofFIG. 26C, the optical device 2692 is configured to diffract the inputlight 2620 to illuminate the display 2404 at an incident angle −6° (inair). However, different from the optical device 2660 of FIG. 26C, theoptical device 2692 includes a zero order redirection grating structure2694 configured to redirect the display zero order light 2654 into theair upwards at a redirection angle of +75°, e.g., redirected zero orderlight 2696. Accordingly, there is larger Fresnel reflection of zeroorder light 2698 back into the optical device 2692, which can beabsorbed by the optical absorber 2669.

When light with p polarization is incident at a Brewster's angle at aninterface between a larger refractive index medium and a smallerrefractive index medium, there is no Fresnel reflection for the lightwith p polarization.

FIG. 27A illustrates an example system 2700 of redirecting display zeroorder light with p polarization to transmit into air at a Brewster'sangle. The system 2700 includes an optical device 2710 that can be theoptical device 2410 of FIG. 24. The optical device 2710 includes asubstrate 2712 (e.g., the substrate 2412 of FIG. 24), a transmissivefield grating structure 2714 (e.g., the transmissive field gratingstructure 2414 of FIG. 24), and a zero order redirection gratingstructure 2716 (e.g., the zero order redirection grating structure 2416of FIG. 24). The optical device 2710 can include a cover glass 2718 onthe zero order redirection grating structure 2716.

Same as the transmissive field grating structure 2614 of the opticaldevice 2610 of FIG. 26A, the transmissive field grating structure 2714of the optical device 2710 diffracts the input light 2620 from theilluminator 2406 to illuminate the display 2404 with an incident angle−6° (in air). A first portion of the input light 2620 illuminating onmodulated display elements of the display 2404 is diffracted to transmitthrough the optical device 2710 (including the zero order redirectiongrating structure 2716) to become diffracted first order light 2701 thatforms a holographic light field 2702. A second portion of the inputlight 2620 illuminating on gaps of the display 2404 is reflected to comeoff the display 2404 as display zero order light 2704. The display zeroorder light 2704 can have p polarization state. In some cases, the inputlight 2620 from the illuminator 2406 has p polarization state. In somecases, the optical device 2710 includes one or more optical polarizingdevices (e.g., polarizers, retarders, waveplates, or a combinationthereof) configured to control a polarization state of the diffractedinput light 2620 to be p polarization. In some implementations, theoptical device 2710 includes an optical retarder (e.g., a broad-bandhalf-wave retarder) followed by an optical polarizer (e.g., a linearpolarizer). The optical retarder is configured to rotate each color oflight from s polarization to p polarization, e.g., with correspondingefficiencies, and the optical polarizer is configured to absorb whateverpercentage of each color of light has not been rotated from spolarization to p polarization.

Different from the zero order redirection grating structure 2616 of FIG.26A, the zero order redirection grating structure 2716 redirects (ordiffracts) the display zero order light 2654 with a Brewster's angle,e.g., approximately −37° in glass, at the interface between the coverglass 2718 and the air. Thus, there is no Fresnel reflection of theredirected display zero order light back to the optical device 2710, andalmost all the redirected display zero order light is transmitted intothe air at the Brewster's angle of approximately −57°, e.g., redirectedzero order light 2706.

FIGS. 27B-27C illustrate examples of redirecting display zero orderlight with s polarization with an optically polarizing device such as anoptical retarder for transmission at a Brewster's angle. When thedisplay zero order light comes off the display 2404 with s polarization,an optical device can include an optical retarder before an interfaceinto air. The optical retarder can convert a polarization state of thedisplay zero order light from s polarization state to p polarizationstate for transmitting at Brewster's angle at the air interface withoutFresnel reflection.

As illustrated in FIG. 27B, a system 2730 includes an optical device2740 that can be the optical device 2410 of FIG. 24. The optical device2740 includes a substrate 2742 (e.g., the substrate 2412 of FIG. 24), atransmissive field grating structure 2744 (e.g., the transmissive fieldgrating structure 2414 of FIG. 24), and a zero order redirection gratingstructure 2746 (e.g., the zero order redirection grating structure 2416of FIG. 24). The optical device 2740 can include a cover glass 2748 onthe zero order redirection grating structure 2746.

Similar to the transmissive field grating structure 2714 of the opticaldevice 2710 of FIG. 27A, the transmissive field grating structure 2744of the optical device 2740 diffracts the input light 2620 from theilluminator 2406 to illuminate the display 2404 with an incident angle−6° (in air). A first portion of the input light 2620 illuminating onmodulated display elements of the display 2404 is diffracted to transmitthrough the optical device 2740 (including the zero order redirectiongrating structure 2746) to become diffracted first order light 2731 thatforms a holographic light field 2732. A second portion of the inputlight 2620 illuminating on gaps of the display 2404 is reflected to comeoff the display 2404 as display zero order light 2734. Different fromthe display zero order light 2704 in FIG. 27A, the display zero orderlight 2734 can have s polarization. In some cases, the input light 2620from the illuminator 2406 has s polarization state. In some cases, theoptical device 2740 includes one or more optically polarizing devicesconfigured to control a polarization state of the diffracted input light2620 to be s polarization.

Different from the optical device 2710 of FIG. 27A, the optical device2740 includes an optical retarder 2747 that is configured to convert apolarization state of the display zero order light 2734 from spolarization to p polarization. In some examples, the polarizationconversion can be achieved using a broadband half-wave retarder, whichcan rotate each color of light from s polarization to p polarizationwith differing efficiencies for each color. The half-wave retarder canbe followed by a “cleanup” linear polarizer to absorb that percentage ofeach color of light which has not been rotated from s polarization to ppolarization. In such a way, the retarder can rotate the polarization oflight emerging from the optical device 2740 to another polarization moresuitable for the best performance of the display 2404, and the linearpolarizer can eliminate light incident upon the display 2404 inpolarizations less suitable for the best performance of the display 240.

In some implementation, as illustrated in FIG. 27B, the optical retarder2747 (and optionally a linear polarizer) is arranged before the zeroorder redirection grating structure 2746 on the substrate 2742. Same asthe zero order redirection grating structure 2716 of FIG. 27A, the zeroorder redirection grating structure 2746 redirects (or diffracts) thedisplay zero order light 2734 with p polarization with a Brewster'sangle, e.g., approximately −37° in glass, at the interface between thecover glass 2748 and the air. Thus, there is no or negligible Fresnelreflection of the redirected display zero order light back to theoptical device 2740, and almost all the redirected display zero orderlight is transmitted into the air at the Brewster's angle ofapproximately −57°, e.g., redirected zero order light 2736.

In some implementations, as illustrated in FIG. 27C, in an opticaldevice 2760 of a system 2750, the optical retarder 2747 is arrangedafter the zero order redirection grating structure 2746 with respect tothe substrate 2742. The zero order redirection grating structure 2746 isarranged between the substrate 2742 and the grating cover glass 2748.The optical retarder 2747 can be arranged between the grating coverglass 2748 and a retarder cover glass 2762. Same as the zero orderredirection grating structure 2716 of FIG. 27A, the zero orderredirection grating structure 2746 redirects (or diffracts) the displayzero order light 2734 with a Brewster's angle, e.g., approximately −37°in glass, at the interface between the retarder cover glass 2762 and theair. Thus, there is no or negligible Fresnel reflection of theredirected display zero order light back to the optical device 2760, andalmost all the redirected display zero order light is transmitted intothe air at the Brewster's angle of approximately −57°, e.g., redirectedzero order light 2752.

FIG. 28 illustrates an example system 2800 of redirecting display zeroorder light to an anisotropic transmitter 2820 for absorbing redirecteddisplay zero order light. The anisotropic transmitter 2820 is configuredto transmit a first light beam (e.g., diffracted first order light) withan angle (e.g., less than a half of a viewing angle of a reconstructioncone) smaller than a predetermined angle, and absorb a second light beam(e.g., the redirected display zero order light) with an angle (e.g., aredirection angle) larger than the predetermined angle. Thepredetermined angle is configured to be larger than the half of theviewing angle and smaller than the redirection angle at which thedisplay zero order light is diffracted by an optically redirectingcomponent.

The system 2800 includes an optical device 2810 that can include theoptical device 2410 of FIG. 24. The optical device 2810 includes asubstrate 2812 (e.g., the substrate 2412 of FIG. 24), a transmissivefield grating structure 2814 (e.g., the transmissive field gratingstructure 2414 of FIG. 24), and a zero order redirection gratingstructure 2816 (e.g., the zero order redirection grating structure 2416of FIG. 24). The optical device 2810 can include a cover glass 2818 onthe zero order redirection grating structure 2816.

Same as the transmissive field grating structure 2414 of the opticaldevice 2410 of FIG. 24, the transmissive field grating structure 2814 ofthe optical device 2810 diffracts the input light 2620 from theilluminator 2406 to illuminate the display 2404 with an incident angle,e.g., −6° in air. A first portion of the input light 2620 illuminatingon modulated display elements of the display 2404 is diffracted totransmit through the optical device 2810 (including the zero orderredirection grating structure 2816) to become diffracted first orderlight 2801 that forms a holographic light field 2802. The incident angleis configured to be larger than a half of the viewing angle of thereconstruction cone corresponding to the holographic light field 2802. Asecond portion of the input light 2620 illuminating on gaps of thedisplay 2404 is reflected to come off the display 2404 as at least apart of display zero order light 2804. Similar to the zero orderredirection grating structure 2416 of FIG. 24, the zero orderredirection grating structure 2816 redirects (or diffracts) the displayzero order light 2804 with a redirection angle substantially larger thanthe incident angle, e.g., an angle corresponding to approximately 75° inair.

Different from the optical device 2410 of FIG. 24, the optical device2810 can include the anisotropic transmitter 2820 configured to transmitthe diffracted first order light 2801 and absorb the display zero orderlight 2804. In some examples, the anisotropic transmitter 2820 includesa louver film configured to have a predetermined angle (or a pass angle)approximately ±30° in air or approximately ±20° in acrylic. Theanisotropic transmitter 2820 substantially transmits the diffractedfirst order light 2801, e.g., at approximately ±5° in air (approximately±3° in acrylic), and absorbs the display zero order light 2804, e.g.,approximately 75° in air. The anisotropic transmitter 2820 can be indexmatched to the cover glass 2818, such that there is no significantFresnel reflection from a surface of the anisotropic transmitter 2820back into the optical device 2810 for the display zero order light 2804having either s-polarization or p-polarization state. Louvers in thelouver film can be also index matched to the transmissive material ofthe louver film to eliminate Fresnel reflections off the louvers.

In the previous examples shown in FIGS. 26A-26E, 27A-27B, and FIG. 28,the zero order redirection grating structures are configured to diffractdisplay zero order light at redirection angles smaller than a criticalangle for total internal reflection at an interface into air.

FIG. 29 illustrates an example system 2900 of redirecting display zeroorder light to totally reflect the display zero order light. Similar tothe optical device 2610 of FIG. 26A, an optical device 2910 of thesystem 2900 includes a transmissive field grating structure 2914 formedon a substrate 2912 and configured to diffract the input light 2620 toilluminate the display 2404 at an incident angle, e.g., −6° in air andapproximately −4° in glass.

However, different from the optical device 2610 of FIG. 26A, the opticaldevice 2910 includes a zero order redirection grating structure 2916configured to redirect display zero order light 2904 at a redirectionangle, e.g., approximately +60° in glass, larger than a critical anglefor total internal reflection in glass, e.g., approximately 41° for atransition from a cover glass 2918 to air at a high-to-low indexinterface 2919. Thus, display zero order light 2904 is totally reflectedback at the interface 2919, and Fresnel reflection of the display zeroorder light 2906 can be absorbed by an optical absorber 2920 (e.g., theoptical absorber 2619 of FIG. 26A) formed on an edge of the opticaldevice 2910. In contrast, a portion of the input light 2620 illuminatingon modulated display elements of the display 2404 is diffracted totransmit through the optical device 2910 (including the zero orderredirection grating structure 2916) to become diffracted first orderlight 2901 that forms a holographic light field 2902, without thedisplay zero order light 2904.

Input light illuminating a display can include multiple different colorsof light, e.g., red, green, and blue. The different colors of light canbe sequentially incident on the display, and corresponding differentcolor holographic data (or holograms) can sequentially modulate displayelements of the display. As described above, an optically diffractivedevice, e.g., the optically diffractive device 598 of FIG. 5H, can beconfigured to diffract the different colors of light to illuminate thedisplay, and can also be configured to reduce color crosstalk among thedifferent colors of light. For example, the optically diffractive device598 includes multiple holographic gratings for the different colors indifferent recording layers, e.g., as illustrated in FIGS. 9A to 12C. Insome examples, as described above with respect to FIGS. 9A to 10B, theoptically diffractive device can include multiple holographic gratingswith one or more color-selective polarizers to suppress (e.g., eliminateor minimize) color crosstalk. In some examples, as described above withrespect to FIGS. 11 to 12C and 15, the optically diffractive device caninclude multiple holographic gratings with one or more reflective layersfor light of different colors incident at respective incident angles tosuppress color crosstalk and zero order light.

Similarly, an optically redirecting device can be also configured toredirect different colors of display zero order light out ofcorresponding holographic scenes and can also be configured to reducecolor crosstalk among the different colors of display zero order light,e.g., by redirecting the different colors of display zero order light todifferent directions away from the holographic scenes in plane and/or inspace. In the following, FIGS. 30A-30B, 31A-31B, 32, and 33 illustratedifferent examples of implementations.

FIGS. 30A-30B illustrate examples of redirecting two different colors(e.g., blue and red) of display zero order light to different directionsaway from a holographic scene.

As illustrated in FIG. 30A, similar to the system 2400 of FIG. 24, asystem 3000 includes a computer 2401 (e.g., the computer 2401 of FIG.24), a controller 3002 (e.g., the controller 2402 of FIG. 24), areflective display 3004 (e.g., the reflective display 2404 of FIG. 24),and an illuminator 3006 (e.g., the illuminator 2406 of FIG. 24). Thesystem 3000 also includes an optical device 3010 that can include anoptically diffractive device, e.g., the optically diffractive device 900of FIGS. 9A and 9B or 1100 of FIG. 11. In some implementations, asillustrated in FIG. 30A, the optical device 3010 includes a transmissivefield grating structure 3014 on a substrate 3012 (e.g., the substrate2412 of FIG. 24). The transmissive field grating structure 3014 caninclude two corresponding different gratings for the two differentcolors of light.

The controller 3002 is configured to receive graphic data correspondingto one or more objects from the computer 3001 (e.g., by using a 3Dsoftware application such as Unity), perform computation on the graphicdata, generate and transmit control signals for modulation to thedisplay 3004 through a memory buffer 3003. The controller 3002 is alsocoupled to the illuminator 3006 and configured to provide a timingsignal 3005 to activate the illuminator 3006 to provide input light3020. The input light 3020 is then diffracted by the transmissive fieldgrating structure 3014 of the optical device 3010 to illuminate thedisplay 3004. A first portion of the input light 3020 incident ondisplay elements of the display 3004 is diffracted by the display 3004,and diffracted first order light 3021 forms a holographic light field3022 towards a viewer. The holographic light field 3022 can correspondto a reconstruction cone (or frustum) that has a viewing angle. A secondportion of the input light 3020 incident on gaps of the display 3004 isreflected by the display 3004 to become at least a part of display zeroorder light 3024.

The transmissive field grating structure 3014 is configured to diffractthe different colors of input light 3020 from the illuminator 3006 outto illuminate the display 3004 off axis at an incident angle, e.g., −6°in air or approximately −4° in glass, larger than a half of a viewingangle of the reconstruction cone (or frustum). By applying the thirdtechnique, the diffracted first order light 3021 comes off the display3004 in the same manner as that when the input light 3020 is incident onaxis at normal incidence, while the display zero order light 3024 comesoff at a reflected angle that is identical to the incident angle, whichis outside of the reconstruction cone.

As illustrated in FIG. 30A, the system 3000 can include an opticallyredirecting structure having corresponding zero order redirectiongratings 3016 and 3018 for different colors (blue and red) of light.Each zero order redirection grating 3016, 3018 can be similar to theredirection grating 2416 of FIG. 24, and configured to diffract a firstlight beam having an angle identical to a predetermined angle with asubstantially larger diffraction efficiency at a diffraction angle thana second light beam having an angle different from the predeterminedangle. Each zero-order redirection grating 3016, 3018 can be aholographic grating such as a Bragg grating for a corresponding color oflight.

As illustrated in FIG. 30A, the zero order redirection grating 3016 isconfigured to diffract blue color display zero order light at areflected angle (identical to the incident angle) of at a diffractionangle of +45° in air (approximately +28° in glass), e.g., redirectedblue zero order display light 3026. The zero order redirection grating3018 is configured to diffract red color display zero order light fromapproximately −6° in air (approximately −4° in glass) to approximately−45° (approximately −28° in glass), e.g., redirected red display zeroorder light 3028.

The zero order redirection gratings 3016, 3018 can be sequentiallyarranged on the substrate 3012 on an opposite side of the transmissivefield grating structure 3014. As light with a shorter wavelength tendsto crosstalk more strongly off gratings intended for longer wavelengths,the zero order redirection grating 3016 for blue color of light can bearranged closer to the display than the zero order redirection grating3018 for red color. The two zero order redirection gratings 3016, 3018can have substantially dissimilar fringe-plane tilts, which can reducecolor crosstalk.

In some implementations, as illustrated in FIG. 30A, each zero orderredirection grating 3016, 3018 for a different color of light isrecorded in a corresponding recording material, e.g., photosensitivepolymer, and protected by a corresponding cover glass 3017, 3019.

In some implementations, as illustrated in FIG. 30B, each zero orderredirection grating 3046, 3048 of an optical device 3040 in a system3030 for a different color of light is recorded in a same recordingmaterial, e.g., photosensitive polymer, and protected by a cover glass3047. The zero order redirection grating 3046 can be same as the zeroorder redirection grating 3016 and configured to diffract blue colordisplay zero order light from approximately −6° in air (approximately−4° in glass) to approximately +45° (approximately +28° in glass), e.g.,redirected blue display zero order light 3036. The zero orderredirection grating 3048 can be same as the zero order redirectiongrating 3018 and configured to diffract red color display zero orderlight from approximately −6° in air (approximately −4° in glass) toapproximately −45° (approximately −28° in glass), e.g., redirected reddisplay zero order light 3038.

The optical devices 3010, 3040 can include optical absorbers (e.g., theoptical absorber 2619 of FIG. 26A) on edges of the optical devices 3010,3040, to reduce Fresnel reflection at the interface between the coverglass and the air.

FIGS. 31A-31B illustrate example systems 3100 and 3150 of redirectingthree different colors (blue, green, red) of display zero order light todifferent directions away from a holographic scene in a same plane.Compared to a system for two different colors of light, e.g., asillustrated in FIG. 30A or 30B, a system for three different colors oflight includes an optical diffractive structure including threedifferent diffraction gratings for diffracting the three colors of inputlight to illuminate a display at a same incident angle, and an opticalredirecting structure including three different zero order redirectiongratings for diffracting three colors of display zero order light atdifferent diffraction angles towards different directions.

As illustrated in FIG. 31A, similar to the system 3000 of FIG. 30A, asystem 3100 includes a computer 3101 (e.g., the computer 3101 of FIG.30A), a controller 3102 (e.g., the controller 3002 of FIG. 30A), areflective display 3104 (e.g., the reflective display 3004 of FIG. 30A),and an illuminator 3106 (e.g., the illuminator 3006 of FIG. 30A). Thesystem 3100 also includes an optical device 3110 that can include anoptically diffractive device, e.g., the optically diffractive device1000 of FIGS. 10A and 10B, 1200 of FIG. 12A, 1250 of FIG. 12B, or 1270of FIG. 12C, or 1500 of FIG. 15. In some implementations, as illustratedin FIG. 31A, the optical device 3110 includes a transmissive fieldgrating structure 3112 on a substrate 3111. The transmissive fieldgrating structure 3112 can include three corresponding differentgratings for the three different colors of light.

The controller 3102 is configured to receive graphic data correspondingto one or more objects from the computer 3101 (e.g., by using a 3Dsoftware application such as Unity), perform computation on the graphicdata, generate and transmit control signals for modulation to thedisplay 3104 through a memory buffer 3103. The controller 3102 is alsocoupled to the illuminator 3106 and configured to provide a timingsignal 3105 to activate the illuminator 3106 to provide input light3120. The input light 3120 is then diffracted by the transmissive fieldgrating 3112 of the optical device 3110 to illuminate the display 3104.A first portion of the input light 3120 incident on display elements ofthe display 3104 is diffracted by the display 3104, and diffracted firstorder light 3121 forms a holographic light field 3122 towards a viewer.The holographic light field 3122 can correspond to a reconstruction cone(or frustum) that has a viewing angle. A second portion of the inputlight 3120 incident on gaps of the display 3104 is reflected by thedisplay 3104 to become display zero order light 3123.

The transmissive field grating 3112 is configured to diffract thedifferent colors of input light 3120 from the illuminator 3106 out toilluminate the display 3104 off axis at an incident angle, e.g., −6° inair or approximately −4° in glass, larger than a half of a viewing angleof the reconstruction cone (or frustum). By applying the thirdtechnique, the diffracted first order light 3121 comes off the display3104 in the same manner as that when the input light 3120 is incident onaxis at normal incidence, while the display zero order light 3123 comesoff at a reflected angle that is identical to the incident angle, whichis outside of the reconstruction cone.

As illustrated in FIG. 31A, the system 3100 can include an opticallyredirecting structure having three corresponding zero order redirectiongratings 3114, 3116, and 3018 for the different colors (blue, green, andred) of light. Each zero order redirection grating 3114, 3116, 3118 canbe similar to the redirection grating 2416 of FIG. 24. Each zero-orderredirection grating 3114, 3116, 3118 can be a holographic grating suchas a Bragg grating for a corresponding color of light.

The zero order redirection gratings 3114, 3116, 3118 can be sequentiallyarranged on the substrate 3111 on an opposite side of the transmissivefield grating structure 3112. In some implementations, as illustrated inFIG. 31A, each zero order redirection grating 3114, 3116, 3118 for adifferent color of light (blue, green, red) is recorded in acorresponding recording material, e.g., photosensitive polymer, andprotected by a corresponding cover glass 3113, 3115, 3117. As notedabove, the zero order redirection gratings 3114, 3116, 3118 for thethree different colors of light can be recorded in a same recordingmaterial, e.g., photosensitive polymer, and protected by a cover glass.The three zero order redirection gratings 3114, 3116, 3118 can havesubstantially dissimilar fringe-plane tilts, which can reduce colorcrosstalk.

As illustrated in FIG. 31A, the blue color zero order redirectiongrating 3114 is configured to diffract blue color display zero orderlight from approximately −6° in air (approximately −4° in glass) toapproximately +45° (approximately +28° in glass), e.g., redirected bluedisplay zero order light 3124. The green color zero order redirectiongrating 3116 is configured to diffract green color display zero orderlight from approximately −6° in air (approximately −4° in glass) toapproximately −45° (approximately −28° in glass), e.g., redirected greendisplay zero order light 3126. The red color zero order redirectiongrating 3118 is configured to diffract red color display zero orderlight from approximately −6° in air (approximately −4° in glass) to theBrewster's angle approximately −57° (approximately −37° in glass), e.g.,redirected red display zero order light 3128. If the red color displayzero order light has p polarization state, the red color display zeroorder light can be totally transmitted into the air. The optical device3110 can include one or more optical absorbers (e.g., the opticalabsorber 2619 of FIG. 26A) on one or more edges of the optical device3110 to reduce Fresnel reflection of the blue and green colors ofdisplay zero order light at the interface between the cover glass andthe air.

If all the three colors of display zero order light have p polarizationstate, e.g., when the input light is p polarized, an optical redirectingdevice can include zero order redirection gratings for the threedifferent colors of display zero order light configured to diffract thethree different colors of display zero order light into air all at theBrewster's angle, which can reduce Fresnel reflection. One or morediffractive gratings can be used together to redirect a particular colorof light.

As illustrated in FIG. 31B, an optical device 3160 of a system 3150includes a blue color redirection grating 3164, a pair of green colorredirection grating 3166-1, 3166-2, and a red color redirection grating3168, which are recorded in corresponding recording media and protectedby corresponding cover glasses 3163, 3165-1 and 3165-2, and 3167. Theblue color zero order redirection grating 3164 is configured to diffractblue color display zero order light from approximately +6° in air(approximately +4° in glass) to the Brewster's angle of approximately−57° in air (approximately −37° in glass), e.g., redirected blue displayzero order light 3154. Green color display zero order light is firstdiffracted by first green color zero order redirection grating 3166-1from approximately +6° in air (approximately +4° in glass) toapproximately +70° (approximately +38° in glass), and then diffracted bysecond green color zero order redirection grating 3166-2 to theBrewster's angle of approximately −57° in air (approximately −37° inglass), e.g., redirected green display zero order light 3156. The redcolor zero order redirection grating 3168 is configured to diffract redcolor display zero order light from approximately +6° in air(approximately +4° in glass) to the Brewster's angle of approximately+57° in air (approximately +37° in glass), e.g., redirected red displayzero order light 3158. The four zero order redirection gratings 3164,3166-1, 3166-2, and 3168 can have substantially dissimilar fringe-planetilts, which can reduce color crosstalk.

To reduce color crosstalk among different colors of display zero orderlight, an optical redirecting device can be configured to redirect thedifferent colors of display zero order light towards differentdirections in a sample plane, as illustrated in FIGS. 30A-30B and31A-31B. The optical redirecting device can also be configured toredirect the different colors of display zero order light towardsdifferent planes in space, as illustrated in FIG. 32 below.

FIG. 32 illustrates an example system 3200 including an optical device3210 of redirecting three different colors (e.g., blue, green, and red)of display zero order light to different directions away fromcorresponding holographic scenes in space.

Similar to the optical device 3110 of FIG. 31A, the optical device 3210includes a transmissive field grating structure 3212 that is same as thetransmissive field grating structure 3112 of FIG. 31A and configured todiffract each color input light to illuminate the display 3104 off axisat an incident angle, e.g., −6° in air or approximately −4° in glass,larger than a half of a viewing angle of the reconstruction cone (orfrustum). By applying the third technique, the diffracted first orderlight comes off the display 3104 in the same manner as that when theinput light is incident on axis at normal incidence. As noted above,light with a larger wavelength corresponds to a larger viewing angle. Asillustrated in FIG. 32, blue color diffracted first order light forms ablue color holographic light field 3220, green color diffracted firstorder light forms a green color holographic light field 3222, and redcolor diffracted first order light forms a red color holographic lightfield 3224.

Similar to the optical device 3110 of FIG. 31A, the optical device 3210includes blue, green, red color redirection gratings 3214, 3216, 3218recorded in different recording media and sequentially arranged on anopposite side of a substrate 3211 with respect to the transmissive fieldgrating structure 3212. The blue, green, red color redirection gratings3214, 3216, 3218 are protected by corresponding blue, green, red coverglasses 3213, 3215, 3217. However, different from the redirectiongratings 3114, 3116, 3118 of FIG. 31A, the redirection gratings 3214,3216, 3218 redirect corresponding colors of display zero order lightinto different planes.

For example, as illustrated in FIG. 32, the blue color redirectiongrating 3214 diffracts the blue color display zero order light fromapproximately −6° in air (approximately −4° in glass) to an upwardsBrewster's angle of approximately +57° in air (approximately +37° inglass), e.g., upwards redirected blue color zero order light 3230. Thered color redirection grating 3218 redirects the red color display zeroorder light from approximately −6° in air (approximately −4° in glass)to a downwards Brewster's angle of approximately −57° in air(approximately −37° in glass), e.g., downwards redirected red color zeroorder light 3234. The green color redirection grating 3216 redirects thegreen color display zero order light from approximately −6° in air(approximately −4° in glass) to a rightwards Brewster's angle(approximately +57° in air, approximately +37° in glass), e.g.,rightwards redirected green color zero order light 3232, which isorthogonal to the plane of the upwards redirected blue color zero orderlight 3230 and downwards redirected red color zero order light 3234.Note that the blue and red color redirection gratings 3214, 3218 havedifferent fringe-plane tilts and/or orientations than the green colorredirection grating 3216, which can suppress color crosstalk.

FIG. 33 illustrates another example system 3300 of redirecting threedifferent colors of display zero order light to different directionsaway from a holographic scene using at least one switchable grating forat least one corresponding color display zero order light.

Similar to the optical device 3110 of FIG. 31A, an optical device 3310in the system 3300 includes blue, green, red color redirection gratings3314, 3316, 3318 sequentially arranged on an opposite side of thesubstrate 3111 with respect to the transmissive field grating structure3112. The blue, green, red color redirection gratings 3314, 3316, 3318are protected by corresponding blue, green, red cover glasses 3313,3315, 3317. Similar to the blue and red color redirection gratings 3114,3118 of FIG. 31A, the blue and red color redirection gratings 3314, 3318are permanently recorded in corresponding recording media.

However, different from the green color redirection grating 3116 of FIG.31A that is permanently recorded in the corresponding recording medium,the green color redirection grating 3316 is recorded in a switchablerecording material, e.g., an electrically switchable Holographic PolymerDispersed Liquid Crystal (HPDLC) material, and configured to beswitchable between different states. For example, the green colorredirection grating 3316 can be switched to a first state during firstintervals of a field-sequential color (FSC) illumination sequence whenonly green color of light is present. During the first green-onlyintervals, the switchable green color redirection grating 3316 in thefirst state diffracts green color display zero order light fromapproximately −6° in air (approximately −4° in glass) to a downwardsangle of approximately −45° in air (approximately −28° in glass), e.g.,redirected green color display zero order light 3338.

During other intervals of the FSC color illumination sequence, when onlyred or blue color of light is present, the switchable green colorredirection grating 3316 is switched to a second state in which theswitchable green color redirection grating does not diffract red or bluecolor of light. As illustrated in FIG. 32, the blue color redirectiongrating 3314 diffracts the blue color display zero order light fromapproximately −6° in air (approximately −4° in glass) to an upwardsangle of approximately +45° in air (approximately +28° in glass), e.g.,upwards redirected blue color zero order light 3336. The red colorredirection grating 3318 redirects the red color display zero orderlight from approximately −6° in air (approximately −4° in glass) to adownwards angle of approximately −45° in air (approximately −28° inglass), e.g., downwards redirected red color zero order light 3340.Although the redirected red color zero order light 3340 has the samedirection as the redirected green color zero order light 3338, theswitchable green color redirection grating 3316 is switched between thefirst state during all, part, or parts of the first intervals forredirecting the green color of light and the second state during all,part, or parts of the other intervals for transmitting the red or bluecolor of light, which can suppress color crosstalk.

In some implementations, two or more separate switchable gratings can beused for two or more corresponding colors, with fewer or nopermanently-recorded gratings, which may further suppress colorcrosstalk. In some implementations, binary (on/off) switchable gratingscan be replaced by switchable gratings in which a first switched statediffracts a first color, and a second switched state diffracts a secondcolor, which can enable the use of fewer or no permanently recordedgratings.

FIG. 34 is a flowchart of an example process 3400 of suppressing displayzero order light in a holographic scene. The process 3400 can beimplemented in a system for reconstructing 2D or 3D objects. The systemcan be any suitable system, e.g., the system 500 of FIG. 5A, 520 of FIG.5B, 530 of FIG. 5C, 540 of FIG. 5D, 560 of FIG. 5E, 570 of FIG. 5F, 580of FIG. 5G, 590 of FIG. 5H, 590A of FIG. 5I, 590B of FIG. 5J, 590C ofFIG. 5K, 1800 of FIG. 18, 1950 of FIG. 19B, 1980 of FIG. 19C, 2100 ofFIG. 21, 2200 of FIG. 22, 2300 of FIG. 23A, 2350 of FIG. 23B, 2400 ofFIG. 24, 2600 of FIG. 26A, 2630 of FIG. 26B, 2650 of FIG. 26C, 2670 ofFIG. 26D, 2690 of FIG. 26E, 2700 of FIG. 27A, 2730 of FIG. 27B, 2750 ofFIG. 27C, 2800 of FIG. 28, 2900 of FIG. 29, 3000 of FIG. 30A, 3030 ofFIG. 30B, 3100 of FIG. 31A, 3150 of FIG. 31B, 3200 of FIG. 32, or 3300of FIG. 33.

At 3402, a display is illuminated with light. A first portion of thelight illuminates display elements of the display. In some cases, asecond portion of the light illuminates gaps between adjacent displayelements. The display can be the display 1610 of FIG. 16, the displayelements can be the display elements 1612 of FIG. 16, and the gaps canbe the gaps 1614 of FIG. 16.

At 3404, the display elements of the display are modulated with ahologram corresponding to holographic data to diffract the first portionof the light to form a holographic scene corresponding to theholographic data and to suppress display zero order light in theholographic scene. The display zero order light can include reflectedlight from the display, e.g., the second portion of the light reflectedat the gaps. The reflected light from the display can be a main order ofthe display zero order light. The display zero order light can alsoinclude any unwanted or undesirable light, e.g., diffracted light at thegaps, reflected light at surfaces of the display elements, and reflectedlight at a surface of a display cover covering the display. Theholographic scene corresponds to a reconstruction cone (or frustum) witha viewing angle. The hologram is configured such that the display zeroorder light is suppressed in the holographic scene. The hologram can beconfigured such that the diffracted first portion of the light has atleast one characteristic different from that of the display zero orderlight. The at least one characteristic can include at least one of apower density (e.g., as illustrated in FIG. 18), a beam divergence(e.g., as illustrated in FIG. 18), a propagating direction away from thedisplay (e.g., as illustrated in FIGS. 19B, 19C, 20B, and 21-33), or apolarization state.

The display zero order light is suppressed in the holographic scene witha light suppression efficiency. The light suppression efficiency can bedefined as a result of one minus a ratio between an amount of thedisplay zero order light in the holographic scene using the suppressionand an amount of the display zero order light in the holographic scenewithout any suppression. In some examples, the light suppressionefficiency is more than a predetermined percentage that is one of 50%,60%, 70%, 80%, 90%, or 99%. In some examples, the light suppressionefficiency is 100%.

In some implementations, the process 3400 further includes: for each ofa plurality of primitives corresponding to an object, determining anelectromagnetic (EM) field contribution to each of the display elementsof the display by computing, in a global three-dimensional (3D)coordinate system, EM field propagation from the primitive to thedisplay element, and for each of the display elements, generating a sumof the EM field contributions from the plurality of primitives to thedisplay element. The holographic data can include the sums of the EMfield contributions for the display elements of the display from theplurality of primitives of the object. When the display is phasemodulated, the holographic data can include respective phases for thedisplay elements of the display. The holographic scene can include areconstructed object corresponding to the object. The holographic datacan include information of two or more objects.

In some implementations, as discussed above with respect to the firsttechnique, “phase calibration,” the hologram can be configured byadjusting the respective phases for the display elements to have apredetermined phase range, e.g., [0, 2π]. In some implementations, therespective phases can be adjusted according to the expression (15)below:

Ø_(a) =AØ _(i) +B,

where Ø_(i) represents an initial phase value of a respective phase,Ø_(a) represents an adjusted phase value of the respective phase, and Aand B are constants for the respective phases. The constants A and B canbe adjusted such that the light suppression efficiency for theholographic scene is maximized or larger than a predetermined threshold,e.g., 50%, 60%, 70%, 80%, 90%, or 99%. In some implementations, theconstants A and B are adjusted according to a machine vision algorithmor a machine learning algorithm.

In some implementations, as discussed above with respect to the secondtechnique, “zero order beam divergence,” an optically divergingcomponent is arranged downstream the display. The optically divergingcomponent can be a defocusing element including a concave lens. e.g.,the concave lens 1802 of FIG. 18. The optically diverging component canbe a focusing element including a convex lens. The diffracted firstportion of the light is guided through the optically diverging componentto form the holographic scene, while the display zero order light isdiverged in the holographic scene. The light illuminating the displaycan be collimated, and the display zero order light can be collimatedbefore arriving at the optically diverging component, and the hologramis configured such that the diffracted first portion of the light isconverging before arriving at the optically diverging component. Theoptically diverging component can be a focusing element including acylindrical lens. The optically diverging component can be a lensletarray including concave, convex, or cylindrical lenses, or a combinationthereof. The optically diverging component can be one or moreHolographic Optical Elements (HOEs), either added to the optical device,or incorporated within one or more of the other diffractive layers ofthe optical device. The one or more HOEs can be configured to converge,diverge or linearly focus light, or to impose a more complicatedtransfer function on the optically diverging component such as directingthe display zero order light to a region or regions outside thereconstruction cone of the holographic scene. The region can include anannular or peripheral region or parts of an annular or peripheralregion. The light illuminating the display can be collimated, and thehologram can be configured such that the diffracted first portion of thelight is shaped with a shaping effect before arriving at the opticallydiverging component such that the effect of the optically divergingcomponent on the first portion of the light compensates the shapingeffect.

In some examples, the hologram is configured by adding a virtual lens,e.g., by adding a corresponding phase to the respective phase for eachof the display elements, and the corresponding phases for the displayelements are compensated by the optically diverging component such thatthe holographic scene corresponds to the respective phases for thedisplay elements. The corresponding phase for each of the displayelements can be expressed by the expression (16) below:

${\varnothing = {\frac{\pi}{\lambda f}\left( {{ax^{2}} + {by^{2}}} \right)}},$

where Ø represents the corresponding phase for the display element, λrepresents a wavelength of the light, f represents a focal length of theoptically diverging component, x and y represent coordinates of thedisplay element in a coordinate system, and a and b represent constants.

In some examples, the hologram is configured in a 3D softwareapplication, e.g., Unity, by moving a configuration cone with respect tothe display with respect to a global 3D coordinate system along adirection perpendicular to the display with a distance corresponding toa focal length of the optically diverging component. The configurationcone corresponds to the reconstruction cone and has an apex angleidentical to the viewing angle. The software application can generateprimitives for objects based on the moved configuration cone in theglobal 3D coordinate system.

The process 3400 can include displaying the holographic scene on atwo-dimensional (2D) screen, e.g., the projection screen 1830 of FIG.18, spaced away from the display along the direction perpendicular tothe display. The 2D screen can be moved along the direction to obtaindifferent slices of the holographic scene on the 2D screen.

The process 3400 can further include guiding the light to illuminate thedisplay. In some examples, the light is guided by a beam splitter, e.g.,the beam splitter 1810 of FIG. 18, to illuminate the display, and thediffracted first portion of the light and the display zero order lighttransmit through the beam splitter.

In some implementations, the display is illuminated with the light atnormal incidence, e.g., as illustrated in FIG. 18 or 19A. In someimplementations, the display is illuminated with the light at anincident angle that can be larger than a half of the viewing angle, asillustrated in FIG. 19B or 19C.

In some implementations, as discussed above with respect to the thirdtechnique, “zero order light deviation,” the hologram is configured suchthat the diffracted first portion of the light forms the reconstructioncone that is the same as a reconstruction cone to be formed by thediffracted first portion of the light if the light is normally incidenton the display, while the reflected second portion of the light comesoff the display at a reflected angle identical to the incident angle, asillustrated in FIG. 19B or 19C.

In some examples, the hologram is configured by adding a virtual prism,e.g., by adding a corresponding phase to the respective phase for eachof the display elements, and the corresponding phases for the displayelements are compensated by the incident angle such that the holographicscene corresponds to the respective phases for the display elements. Thecorresponding phase for each of the display elements can be expressed bythe expression (17) below:

${\varnothing = {\frac{2\pi}{\lambda}\left( {{x\;\cos\;\theta} + {y\;\cos\;\theta}} \right)}},$

where Ø represents the corresponding phase for the display element, λrepresents a wavelength of the light, x and y represent coordinates ofthe display element in the global 3D coordinate system, and θ representsan angle corresponding to the incident angle.

In some examples, the hologram is configured by moving the configurationcone with respect to the display with respect to the global 3Dcoordinate system, e.g., as illustrated in FIG. 20B, by rotating theconfiguration cone by a rotation angle with respect to a surface of thedisplay with respect to the global 3D coordinate system, the rotationangle corresponding to the incident angle.

In some implementations, as discussed above with respect to the fourthtechnique, “zero order light blocking,” the display zero order light isblocked to appear in the holographic scene. The light suppressionefficiency for the holographic scene can be 100%.

In some examples, an optically blocking component is arranged downstreamthe display. The optically blocking component can include a plurality ofmicrostructures or nanostructures. The optically blocking component caninclude a metamaterial layer, e.g., the metamaterial layer 2316 of FIGS.23A-23B, or a louver film, e.g., the anisotropic transmitter of FIG. 28.The optically blocking component is configured to transmit a first lightbeam having an angle smaller than a predetermined angle and block asecond light beam having an angle larger than the predetermined angle,and the predetermined angle is smaller than the incident angle andlarger than the half of the viewing angle. Thus, as illustrated in FIGS.23A, 23B, the display zero order light is blocked by the opticallyblocking component, and the diffracted first portion of the lighttransmits through the optically blocking component with a transmissionefficiency to form the holographic scene. The transmission efficiency isno less than a predetermined ratio, e.g., 50%, 60%, 70%, 80%, 90%, or99%.

In some implementations, the process 3400 further includes: guiding thelight to illuminate the display by guiding the light through anoptically diffractive component on a substrate configured to diffractthe light out with the incident angle. The optically diffractivecomponent can the outcoupler 1914 of FIG. 19A, 1964 of FIG. 19B or 19C,or the transmissive field grating structure 2414 of FIG. 24. In someexamples, the light is guided through a waveguide coupler, e.g., theincoupler 1916 of FIG. 19A, or 1966 of FIG. 19B or 19C, to the opticallydiffractive component. In some examples, the light is guided through acoupling prism, e.g., the coupling prism 2111 of FIG. 21 or 2311 of FIG.23A or 23B, to the optically diffractive component. In some examples,the light is guided through a wedged surface of the substrate to theoptically diffractive component, e.g., as illustrated in FIG. 22.

As illustrated in FIG. 23A or 23B, the optically diffractive componentis formed on a first surface of the substrate facing to the display, andthe optically blocking component is formed on a second surface of thesubstrate that is opposite to the first surface.

In some implementations, as discussed above with respect to the fifthtechnique, “zero order light redirection,” an optically redirectingcomponent is arranged downstream the display and configured to transmitthe diffracted first portion of the light to form the holographic sceneand redirect the display zero order light away from the holographicscene. The optically redirecting component can be the zero orderredirection grating structure 2416 of FIG. 24, 2616 of FIG. 26A, 2646 ofFIG. 26B, 2666 of FIG. 26C or 26D, 2694 of FIG. 26E, 2716 of FIG. 27A,2746 of FIG. 27B or 27C, 2816 of FIG. 28, 2916 of FIGS. 29, 3016 and3018 of FIG. 30A, 3046 and 3048 of FIG. 30B, 3114, 3116, and 3118 ofFIG. 31A, 3164, 3166-1, 3166-2, and 3168 of FIG. 31B, or 3214, 3216, and3218 of FIG. 32, or 3314, 3316, and 3318 of FIG. 33.

The optically redirecting component can be configured to diffract afirst light beam having an angle identical to a predetermined angle witha substantially larger diffraction efficiency than a second light beamhaving an angle different from the predetermined angle, and thepredetermined angle is substantially identical to the incident angle.The optically redirecting component can include one or more holographicgratings such as Bragg gratings.

In some implementations, the optically diffractive component is formedon a first surface of the substrate facing towards the display, and theoptically redirecting component is formed on a second surface of thesubstrate that is opposite to the first surface, e.g., as illustrated inFIGS. 24 to 33.

The optically redirecting component is configured such that the displayzero order light is diffracted outside of the holographic scene in athree-dimensional (3D) space along at least one of an upward direction,a downward direction, a leftward direction, a rightward direction, or acombination thereof. The light suppression efficiency for theholographic scene can be 100%. In some examples, as illustrated in FIG.26A, the incident angle of the light is negative, e.g., −6° in air, anda diffraction angle of the display zero order light diffracted by theoptically redirecting component is negative, e.g., −45° in air. In someexamples, as illustrated in FIG. 26B, the incident angle of the light ispositive, e.g., +6° in air, and a diffraction angle of the display zeroorder light diffracted by the optically redirecting component ispositive, e.g., +45° in air. In some examples, as illustrated in FIG.26C or 26D, the incident angle of the light is negative, e.g., −6° inair, and a diffraction angle of the display zero order light diffractedby the optically redirecting component is positive, e.g., +45° in air.In some examples, the incident angle of the light is positive, +6° inair, and a diffraction angle of the display zero order light diffractedby the optically redirecting component is negative, e.g., −45° in air.

The optically redirecting component can be covered by a secondsubstrate, e.g., the cover glass 2618 of FIG. 26A. The opticallyredirecting component can be configured to redirect the display zeroorder light to an optical absorber, e.g., the optical absorber 2619 ofFIG. 26A or 2649 of FIG. 26B, formed on at least one of a side surfaceof the second substrate or a side surface of the substrate. The secondsubstrate can include an anti-reflective (AR) coating, e.g., the ARcoating 2682 of FIG. 26D, on a surface of the second substrate oppositeto the optically redirecting component. The anti-reflective coating isconfigured to transmit the display zero order light to prevent Fresnelreflection of the display zero order light. An anti-reflective coatingcan also be configured to reduce or eliminate reflections of ambientlight from the viewer and the environment reflected off theviewer-facing front surface of the second substrate, e.g., the ARcoating 2682 of FIG. 26D. The final AR coating can be designed such thatit does not interfere with those of the five techniques as describedherein which depend upon the properties of the final transition into airon the viewer's side. Preventing Fresnel reflection from the frontsurface prevents the viewer seeing themselves and room lights mirroredby the front surface. Deeper surfaces within the optical device involveonly comparatively small refractive index changes, and hence minimalFresnel reflection of the observer and room light back towards theviewer, or the surfaces can also be AR coated, or, as in the case of therear-reflector of the display, the surfaces are behind multipleabsorptive layers, such as linear polarizers, through which ambientillumination can make a double pass and be hence attenuated, an effectwhich can be enhanced by adding to or incorporating within the device alayer of a material with a cumulative optical density in the range 0.2to 1.0.

In some implementations, the display zero order light is p polarizedbefore arriving at the second substrate. As illustrated in FIG. 27A, theoptically redirecting component can be configured to diffract thedisplay zero order light to be incident at a Brewster's angle on aninterface between the second substrate and a surrounding medium, e.g.,air, such that the display zero order light totally transmits throughthe second substrate.

In some implementations, the display zero order light is s polarizedbefore arriving at the second substrate. The process 3400 can furtherinclude: converting a polarization state of the display zero order lightfrom s polarization to p polarization. In some examples, converting thepolarization state of the display zero order light is by an opticalretarder (e.g., the optical retarder 2747 of FIG. 27B) (and optionally alinear polarizer) arranged upstream the optically redirecting componentwith respect to the display. In some examples, converting thepolarization state of the display zero order light is by an opticalretarder (e.g., the optical retarder 2747 of FIG. 27C) (and optionally alinear polarizer) arranged downstream the optically redirectingcomponent with respect to the display. The optical retarder can beformed on a side of the second substrate opposite to the opticallyredirecting component, and the optical retarder can be covered by athird substrate (e.g., the retarder cover glass 2762 of FIG. 27C).

In some implementations, as illustrated in FIG. 28, an opticallyblocking component is formed on a side of the second substrate opposingto the optically redirecting component. The optically blocking componentis configured to transmit the diffracted first portion of the light andto absorb the display zero order light diffracted by the opticallyredirecting component. In some examples, the optically blockingcomponent includes an anisotropic transmitter (e.g., the anisotropictransmitter 2820 of FIG. 28) configured to transmit a first light beamwith an angle smaller than a predetermined angle, and absorb a secondlight beam with an angle larger than the predetermined angle. Thepredetermined angle is larger than half of the viewing angle and smallerthan a diffraction angle at which the display zero order light isdiffracted by the optically redirecting component.

In some implementations, as illustrated in FIG. 29, the opticallyredirecting component is configured to diffract the display zero orderlight to be incident with an angle larger than a critical angle on aninterface between the second substrate and a surrounding medium, suchthat the display zero order light diffracted by the opticallydiffractive component is totally reflected at the interface. An opticalabsorber, e.g., the optical absorber 2920 of FIG. 29, can be formed onside surfaces of the substrate and the second substrate and configuredto absorb the totally reflected display zero order light.

In some implementations, as illustrated in FIGS. 30A to 33, the lightincludes a plurality of different colors of light, and the opticallydiffractive component is configured to diffract the plurality ofdifferent colors of light at the incident angle on the display. Theoptical redirecting component comprises a respective opticallyredirecting subcomponent for each of the plurality of different colorsof light.

In some implementations, as illustrated in FIG. 30B, the respectiveoptically redirecting subcomponents for the plurality of differentcolors of light are recorded in a same recording structure, or inrecording structure which are adjacent and separated only by a thinoptical indexing, contacting, or adhesive layer. In someimplementations, as illustrated in FIGS. 30A, 31A, 31B, 32, 33, therespective optically directing subcomponents for the plurality ofdifferent colors of light are recorded in different correspondingrecording structures which may be separated by cover glasses.

The optical redirecting component can be configured to diffract theplurality of different colors of light at different diffraction anglestowards different directions in a 3D space. In some examples, asillustrated in FIGS. 31A-31B, the optical redirecting component isconfigured to diffract at least one of the plurality of different colorsof light to be incident at at least one Brewster's angle at aninterface. The interface can include one of an interface between a topsubstrate and a surrounding medium or an interface between two adjacentsubstrates.

In some implementations, as illustrated in FIG. 32, the opticalredirecting component is configured to diffract a first color of light(e.g., blue) and a second color of light (e.g., red) within a plane, anda third color of light (e.g., green) orthogonal to the plane.

In some implementations, as illustrated in FIG. 31B, the opticalredirecting component includes at least two different opticallyredirecting subcomponents (e.g., the redirection gratings 3166-1, 3166-2of FIG. 31B) configured to diffract a same color of light of theplurality of different colors of light. The two different opticallyredirecting subcomponents can be sequentially arranged in the opticalredirecting component.

Guiding the light to illuminate the display can include sequentiallyguiding the plurality of different colors of light to illuminate thedisplay in a series of time periods. In some implementations, asillustrated in FIG. 33, the optical redirecting component can include aswitchable optically redirecting subcomponent (e.g., the switchablegreen redirection grating 3316 of FIG. 33) configured to diffract afirst color of light at a first state during all, part, or parts of afirst time period and transmit a second color of light at a second stateduring all, part, or parts of a second time period.

In some implementations, the switchable optically redirectingsubcomponent is configured to diffract a first color of light at a firststate during all, part, or parts of a first time period and diffract asecond color of light at a second state during all, part, or parts of asecond time period.

The plurality of different colors of light can include a first color oflight and a second color of light, the first color of light having ashorter wavelength than the second color of light. In the opticallyredirecting component, a first optically redirecting subcomponent forthe first color of light can be arranged closer to the display than asecond optically redirecting subcomponent for the second color of light,as illustrated in FIGS. 30A to 33.

In some implementations, fringe planes of at least two opticallyredirecting subcomponents for at least two different colors of light areoriented substantially differently.

In some implementations, the optically redirecting component includes: afirst optically redirecting component configured to diffract a firstcolor of light, a second optically redirecting component configured todiffract a second color of light, and at least one optical retarder (andoptionally a linear polarizer) arranged between the first and secondoptically redirecting subcomponent and configured to convert apolarization state of the first color of light such that the first colorof light transmits through the second optically redirecting component.

The reflected second portion of the light has a reflected angleidentical to the incident angle and propagates outside of theholographic scene. In some examples, a half of the viewing angle iswithin a range from −10 degrees to 10 degrees or a range from −5 degreesto 5 degrees. In some examples, the incident angle is −6 degrees or 6degrees.

In some implementations, the optical redirecting component is configuredto allow the display zero order light to pass through unchanged, andredirect the diffracted first portion of the light to form a holographicscene corresponding to a cone or frustum having a predetermined angle,which is away from the display zero order light.

In some implementations, the optical redirecting component is configuredto redirect the display zero order light towards a first direction andredirect the diffracted first portion of the light towards a seconddirection away from the first direction. For example, the diffractedfirst portion of the light can be redirected to be normal to a wedgedsurface of a substrate, and the display zero order light can beredirected to hit the wedged surface beyond a critical angle and henceundergo total-internal-reflection (TIR) back into the substrate.

Additional Aspects of Displaying Reconstructed Three-Dimensional Objects

Implementations of the present disclosure provide a display system fordisplaying reconstructed three-dimensional (3D) objects in a holographiclight field, e.g., the holographic light field 518 of FIG. 5A, 528 ofFIG. 5B, 538 of FIG. 5C, 548 of FIG. 5D, 568 of FIG. 5E, 578 of FIG. 5F,599-1 or 599-2 of FIG. 5H, SI, 5J, or 5K, 2422 of FIG. 24, 2622 of FIG.26A, 2632 of FIG. 26B, 2652 of FIG. 26C, 26D or 26E, 2702 of FIG. 27A,2732 of FIG. 27B or 27C, 2802 of FIG. 28, 2902 of FIG. 29, 3022 of FIG.30A or 30B, 3122 of FIG. 31A or 31B or 33, or 3220, 3222, 3224 of FIG.32. Techniques described herein can improve one or more characteristics(e.g., size or zero order suppression) of the holographic light field tothereby improve a performance of the display system, e.g., by usinglarger reflective displays, using larger gratings, and/or controllinginput light. For illustration purpose only, the techniques are discussedwith reference to the system 3100 in FIG. 31A.

First Exemplary Method—Using Larger Reflective Displays

One method to increase a size of the holographic light field 3122 ofFIG. 31A is to build the same optical geometry using a larger reflectivedisplay 3104 and a proportionately larger substrate 3111 with unchangedbeam angles.

As the linear extent of the reflective display 3104 increases, thefront-area of the substrate 3111 increases as a square of the increasein the linear extent of the reflective display 3104. If the beam anglesand beam distributions remain unchanged, then the thickness of thesubstrate 3111 increases as the increase in the linear extent of thereflective display 3104. As a result, a volume of the substrate 3111 canincrease as a cube of the increase in the linear extent of thereflective display 3104. For example, doubling the width of thereflective display 3104, while maintaining the same width-to-heightaspect ratio of the reflective display 3104 and a proportional thicknessof the substrate 3111, quadruples the front-area of the substrate 3111and increases the volume of the substrate 3111 by a factor of eight.Eventually the large thickness and the high cost of the substrate 3111may become undesirable, e.g., because it may be desirable that thesubstrate 3111 maintains an optical-grade clarity, substantially freefrom significant inclusions, absorption, scatter, birefringence, and/orother visible optical defects or imperfections.

The weight of the substrate 3111 also may become undesirable. Forexample, the substrate 3111 may have a thickness of approximately 20% ofthe height of the reflective display 3104. As an example, for a 686 mm(27″) diagonal reflective display 3104 with a 16:9 aspect-ratio (typicaldimensions for a computer monitor), the substrate 3111 may havedimensions of 598 mm×336 mm×68 mm or greater. If such a substrate 3111were made from a solid block of acrylic with a density of 1.17 to 1.20g/cm³, the weight of substrate 3111 could be at least 16 kg (35 pounds).For a similar 1,650 mm (65″) diagonal reflective display 3104 with the16:9 aspect-ration, the substrate 3111 can be at least 165 mm thick andweigh at least 225 kg (495 pounds), which can be challenging to ship,install, and move. Mounting and support structures for such a block ofacrylic may also be large and heavy.

Further, if all or part of the holographic light field 3122 is projectedinto a viewing space in front of the final cover glass 3113, then it maybe desirable for the holographic light field 3122 to be positionedproportionately further in front of the front cover glass 3113 (e.g.,more than 165 mm in front of the reflective display 3104 with a 1,650 mmdiagonal). This could reduce its field of view and resolution. If alesser, zero, or negative z-axis translation is applied, the holographiclight field 3122 may appear deeper behind the front surface of the frontcover glass 3113.

To address the above issues, the substrate 3111 can be made thinner,which may reduce its mas, cost, and cause the substrate to have lesserconstraints on its z-position and field of view.

In some embodiments, the substrate 3111 can be made of a material with alower density and/or with a refractive index permitting more extremeangles and beam-angle changes for the beams entering, within, andexiting the substrate 3111. For example, a liquid-filled substrate 3111can be used with a liquid, e.g., water or oil, with a refractive indexthat can be smaller (e.g., 17% to 20% smaller) than a refractive indexof acrylic. The liquid can be enclosed in a tank, which may help resolvecertain potential shipping and installation issues because the tank canbe transported empty and then filled in situ.

In certain embodiments, the angle of the input light 3120 as refractedinto the substrate 3111 can be increased for one or more wavelengths ofthe input light 3120. This can allow for the use of a relatively thinsubstrate 3111 for the input light 3120, e.g., to illuminate a same areaof the reflective display 3104. In some cases, it may be desirable tochoose the angle(s) to achieve a particular diffraction efficiencyand/or to meet desired critical-angle properties.

In some embodiments, the substrate 3111 can be wedged, e.g., similar tothe substrate 1252 of FIG. 12B or the substrate 1272 of FIG. 12C, suchthat incident angles of the input light 3120 on the field grating 3112can be relatively large.

In certain embodiments, two or more illuminators can be used toilluminate different regions of the reflective display 3104, e.g.,respectively from upper and lower directions. For example, a firstilluminator 3106 providing first input light 3120 into a first edge-faceof the substrate 3111 (e.g., a lower edge-face of substrate 3111) can beused to illuminate only a first region (e.g., a lower half) of thereflective display 3104. A second illuminator (which can be similar tothe first illuminator 3106) providing second input light (which can besimilar to the first input light 3120) into a second edge-face of thesubstrate 3111 (e.g., an upper edge-face of the substrate 3111) can beused to illuminate only a second region (e.g., an upper half) of thereflective display 3104. Such an arrangement can allow the reflectivedisplay 3104 to be fully illuminated while allowing the substrate 3111to be relatively thin (e.g., allowing the thickness of the substrate3111 to be halved). Optionally, a third, fourth, or greater number ofinput lights, each entering through a different corresponding edge-faceof the substrate 3111 (e.g., left and right edge-faces of the substrate3111), can be used to illuminate, respectively, regions (e.g., a leftregion and a right region, respectively) of the reflective display 3104.

In some embodiments, input light can illuminate different regions of thereflective display 3104 along different optical paths. For example, afirst illuminator 3106, providing first input light 3120 into anedge-face of the substrate 3111 (e.g., a lower edge-face of thesubstrate 3111) and directly illuminating the transmissive field grating3112, can be used in combination with a second illuminator, providingsecond input light into an edge-face of substrate 3111 (which may be thesame edge-face as used by the first input light) but with the secondinput light being initially directed forwards towards the redirectiongrating 3114 and subsequently being reflected back towards thetransmissive field grating 3112 such that the first input lightilluminates a first region (e.g., an upper half) of the reflectivedisplay 3104 and the second input light illuminates a second adjacentregion (e.g., a lower half) of the reflective display 3104. Suchreflection of the second input light may be achieved by using totalinternal reflection (TIR) or a reflective grating at a surface of orprior to the redirection grating 3114 (e.g., by an interface between thesubstrate 3111 and the redirection grating 3114). Alternatively, apartially reflective surface (e.g., a 50:50 or gradient or patternedbeamsplitter) can be incorporated into the substrate 3111 to split asingle input light 3120 within the substrate 3111 into two beams,including a first beam proceeding directly to the transmissive fieldgrating 3112 with a reduced optical power and a second beam initiallyproceeding away from the transmissive field grating 3112, also withreduced optical power, and subsequently being directed back towards thetransmissive field grating 3112, e.g., by TIR or a reflective grating ata surface of or prior to the redirection grating 3114.

In certain embodiments, the diffraction efficiency of the transmissivefield grating 3112 may be patterned such that, when the input light 3120first encounters a sub-region of the transmissive field grating 3112,only a chosen percentage of the input light 3120 is diffracted outtowards the reflective display 3104, while all or part of the remainderof the input light 3120 is reflected back into the substrate 3111. Thereflected input light 3120 in the substrate 3111 is further reflected byTIR off, for example, the front surface of the substrate 3111 backtowards a second sub-region of the transmissive field grating 3112 whichcouples out a second portion towards the reflective display 3104 with adiffraction efficiency adjusted such that two such regions of thetransmissive field grating 3112 illuminate two corresponding sub-regionsof the reflective display 3104 with a substantially similar opticalpower. The above process can be extended to three or more suchsub-regions of the transmissive field grating 3112 and accordingly threeor more corresponding sub-regions of the reflective display 3104.

In some embodiments, light not initially diffracted to a reflectivedisplay is recycled to illuminate the reflective display. For example,the diffraction efficiency of the transmissive field grating 3112 can bepatterned or chosen such that, when the input light 3120 firstencounters a first sub-region of the transmissive field grating 3112,only a chosen percentage of such input light 3120 is diffracted outtowards the reflective display 3104, while all or part of the remainderof the input light 3120 is reflected back into the substrate 3111. Thereflected input light 3120 can eventually make its way (e.g., by TIRwithin substrate 3111 or via a direct path) to a reflective elementattached to or subsequent to an edge face of the substrate 3111 (e.g., amirror or a reflective grating in place of the absorber 1203 of FIG.12B) which reflects it back through the substrate 3111 to reilluminate(directly, or after further TIR or diffractive redirections) the firstsub-region of the transmissive field grating 3112 or a second sub-regionof the transmissive field grating 3112 where the sub-region of thetransmissive field grating 3112 diffracts it out towards the reflectivedisplay 3104.

In some embodiments, each of sub-regions of the reflective display 3104is made of an individual display device (e.g., LCoS) or any otherreflective display device, and the reflective display 3104 is formed bya tiled array of smaller display devices. This can allow differences indiffraction efficiency and hence in device illumination for eachsub-region of the transmissive field grating 3112 to be compensated forby operating such smaller display devices with different reflectivities.

In certain embodiments, a relatively high aspect ratio of the width tothe height of the reflective display is used to increase the size of theholographic light field. Because the thickness of the substrate 3111generally depends on illuminated height of the reflective display 3104but not on the illuminated width of the reflective display 3104, thethickness of the substrate 3111 does not have to be increased if theaspect ratio of the reflective display 3104 is increased such that itswidth is increased without necessarily a corresponding increase in itsheight. For example, rather than the 16:9 aspect ratio of width:height,an aspect ratio of 20:9 may be used. Increasing the aspect ratio of thereflective display 3104 in this manner can increase the size of aholographic light field, because the viewer typically has two eyes in apredominantly horizontal arrangement, affording stereopsis.

In some cases, when multiple viewers observe the holographic light fielddisplay at the same time, the viewers are likely to be positionedside-by-side (rather than one looking over the head of the other), sothe wider field of view afforded by a high-aspect ratio can be suitablefor group viewing. Further, empirically it has been observed that mostviewers of holographic light fields, e.g., casual viewers, are morelikely to move their heads from side to side rather than up and down, soagain a higher aspect ratio with a wider width can be implemented toincrease the performance of the system.

In some cases, a useful and pleasing holographic light field display mayhave a very high aspect ratio (a strip or slit display). A wider aspectratio can be achieved with a comparatively thin substrate 3111, e.g., ifgratings 3112, 3114, 3116, and 3118 are tiled in the horizontaldirection.

In general, irrespective of the aspect ratio of the reflective display3104 (and hence of the substrate 3111 and the gratings 3112, 3114, 3116,and 3118), it is desirable for the width of input light 3110 to besufficient to illuminate the width of the reflective display 3104 (andthe width of the substrate 3111 and the gratings 3112, 3114, 3116, and3118). For low aspect ratios of the reflective display 3104, the inputlight 3120 can have a mildly extended rectangular profile orcross-section (or even a square profile or cross-section), which can beimplemented by masking or otherwise truncating a sufficiently largecircular or elliptical beam profile from the illuminator 3106.

Second Exemplary Method—Using Larger Gratings

If the reflective display 3104 and the substrate 3111 are enlarged, thenthe transmissive field grating 3112 and the display zero-orderredirecting gratings 3114, 3116, and 3118 can also be enlarged to match.

In some embodiments, the transmissive field grating 3112 can be splitinto two or more regions, each utilizing an input light enteringsubstrate 3111 through a different edge face of the substrate 3111 asnoted above.

In certain embodiments, larger gratings 3112, 3114, 3116, and 3118 canbe produced by enlarging corresponding optical elements and recordingmaterials of their respective production systems.

In some embodiments, larger gratings 3112, 3114, 3116, and 3118 can beproduced by tiled optical-recording, in which sub-regions of each of thegratings can be recorded in sequence using smaller optical elements andfull-sized recording materials in a step-and-repeat process. This canallow fore the use of smaller optical components, which are oftenrelatively inexpensive. Additionally or alternatively, this can allowfor the use of lower recording powers (e.g., rather than increasingrecording exposure durations), which can allow for the use of relativelyinexpensive recording laser sources, and/or a relative large range oflaser technologies, wavelengths, and vendors available to provide suchsources. Such tiled-gratings also may be used to provide multipleregions for enlarging the transmissive field grating 3112 using multipleinput lights.

Edges of the tiled sub-regions of gratings can abut each other with aslight gap between the sub-regions of the gratings. Optionally, thesub-regions can join seamlessly, or the sub-regions can overlap slightlyor substantially. Combinations of such approaches are possible. In somecases, slight gaps can be invisible or may have low visibility to theviewer. For example, when the holographic light field 3122 occupiesoptical distances from the viewer which do not include the opticaldistance of the grating from the viewer, the gaps may be out-of-focuswhen the viewer's eyes are focused on the holographic light field 3122.In certain cases, slight overlaps may have little or no visibility tothe viewer. Substantial overlaps, e.g., a 50% overlap, between twosub-regions of the gratings may be implemented to smooth and/or reducethe visibility of the tiling and/or to improve the net uniformity of theoverlapped gratings.

In some cases, to reduce the visibility of such slight gaps or overlapsbetween the tiled sub-regions of gratings, the sub-regions of gratingscan be aligned with gaps between smaller display devices forming thereflective display 3104 as a tiled array of smaller display devices.

In some cases, effectively seamless gratings, with neither a significantgap nor a significant overlap, can be implemented by including one ormore edge-defining elements, e.g., a square, a rectangular, or otherwisea plane-tiling aperture, in the optics of the recording reference and/orobject beams when recording the gratings for a sub-region, andprojecting or re-imaging the edge or edges so formed such that the edgesare substantially in a sharp focus within the recording material duringthe recording of the grating or gratings. Sharply well defined edges canalso be achieved, for example, using reflective or transmissive phasemasks in the optics of the recording reference and/or object beams whenrecording the gratings for a sub-region.

In some embodiments, larger gratings 3112, 3114, 3116, and 3118 can beproduced using mechanical rather than optical means, e.g., embossed,nano-imprinted, or self-assembled structures, and such mechanicallyproduced gratings can also be tiled in one or more dimensions, e.g., bythe use of roller embossing in a roll-to-roll system.

Third Exemplary Method—Controlling Input Light

As noted above, as the aspect ratio of reflective display 3104 isincreased, a more extended rectangular profile for the input light 3110can become desirable, and a more elliptical beam profile from theilluminator 3106 can also become desirable. Because many laser-diodesproduce elliptical beams, in some cases, the desired beam profile fromthe illuminator 3106 can be implemented by rotating the ellipticity oflaser diode sources within the illuminator 3106, e.g., by mechanicallyor optically rotating the laser diode sources within the illuminator3106.

Because many laser diodes emit substantially polarized light, andbecause certain other components of the optical device 3110 may performbetter for a particular polarization orientation (e.g., may require aparticular polarization orientation), it may be desirable to rotate theellipticity and polarization orientation of light sources within theilluminator 3106 independently, e.g., by using a broad-wavelength-bandhalf-wave retarder to rotate the polarization of all of the input light3120, or by using individual narrow-wavelength-band half-wave retardersto rotate the polarization of each color of input light 3120,separately. Because the profile or cross-section of the input light 3120may be quite extensive in both width and height, low cost half-waveplates such as polymer waveplates or liquid-crystal waveplates may bemore suitable than high cost half-wave plates fabricated form forexample quartz.

In some embodiments, the uniformity of the input light 3120 can beimproved by using apodizing optical elements or profile converters,e.g., arrangements of optical elements like lenses or holographicoptical elements (HOEs) or integrating rods to effect, for example,Gaussian to top-hat and/or circular to rectangular profile conversion,or by using polarization recycling elements.

In certain embodiments, anamorphic optics can be implemented. The aspectratio of the reflective display 3104 can be increased to such an extentthat the a desired degree of anamophicity of the input light 3120 mayexceed a threshold degree which can conveniently be provided by costeffective light sources in the illuminator 3160 without masking off andhence wasting an unacceptable proportion of the light source power. Insuch cases, the width of the input light 3120 can be further increasedby the use of anamorphic optics, e.g., anamorphic lenses or cylindricallenses, or HOEs performing as anamorphic or cylindrical lenses ormirrors.

Exemplary System

FIGS. 35A-C illustrate an example system 3500 for displayingreconstructed 3D objects. FIGS. 36A-C show the same views of the system3500 as FIGS. 35A-C, respectively, but with three colors of light (e.g.,red, green, blue) propagate through the system 3500.

A rectangular section of substantially-coaxial elliptical beams 3501 (asillustrated in FIG. 36A) from an illuminator 3501S (e.g., made of threelaser diodes for three different colors such as red, green, and blue) isreflected off a mirror 3502 and then refracted into a first face 3503 ofa prism element 3504. The beams 3501 have a width defined between anupper beam and a lower beam, as illustrated in FIG. 36A. The differentcolors of light beams refracted into the prism element 3504 can bestacked together along a first direction (e.g., as illustrated in FIG.36A) and spaced from (or overlapping with) one another along a seconddirection (e.g., as illustrated in FIG. 36B). A second surface 3505 ofthe prism element 3504 reflects the beams to a third surface 3506 of theprism element 3504 on which one or more transmissive expansion gratings3507 are optically stacked (generally, one grating per color). Eachexpansion grating is illuminated by its corresponding color at arelatively high angle of incidence within the prism element 3504, forexample 68°, and is configured to diffract a portion of its illuminatinglight out towards a series of reflectors 3508. In effect, the gratings3507 expand the original rectangular section of light beams 3501 fromthe laser diodes by a substantial factor (e.g., a factor ofapproximately 6) in one dimension (e.g., in width as illustrated in FIG.36A). Light beams reflected by the third surface 3506 and/or theexpansion gratings 3507 and/or a cover layer applied to the expansiongratings 3507, back into the prism element 3504 can be absorbed by anabsorptive layer 3504A applied to a surface of the prism element 3504(e.g., as illustrated in FIG. 36A).

Because the light incident upon the gratings 3507 is incident at a highangle, the depth of prism element 3504 (e.g., the length of its face3505, part of which at least is reflective) can be comparatively small.The incidence angle can exceed criticality if the light is incident fromair (refractive index ˜1.0) upon the gratings 3507 at such a largeangle, causing all of the incident light to reflect away from thegratings. In the system 3500, the light is incident from the prismelement 3504 that can be made of, for example, glass or acrylic with ahigh refractive index (e.g., ˜1.5), and thus, the incident angle doesnot exceed the critical angle.

In some embodiments, the reflectors 3508 can include three dichroicreflectors, one per color, or two dichroics and a mirror for one color,or one dichroic reflector for two colors and a mirror for one color,that are arranged in the beam (all three colors) 3509 diffracted out byexpansion gratings 3507, to reflect each color into a cover plate 3510attached to a shaped substrate 3511. Each color of light is incident onthe cover plate 3510 at a different angle and over a different region ofthe cover plate 3510, and is refracted into the cover plate 3510 (andthereafter into the shaped substrate 3511) at such angles that thecolors of light subsequently are reflected off, for example, a low-indexlayer formed on the front face 3512 of the shaped substrate 3511, thendiffracted out of three stacked field gratings (one per color) 3513attached to the back face 3514 of the shaped substrate 3511. All threecolors of light are incident on an array of reflective display devices3515 at substantially the same angle for each color and with each colorilluminating substantially the entirety of the reflective area formed byone or more reflective display devices 3515. The reflective displaydevices reflect and diffract each color back through the field gratings3513, through the shaped substrate 3511, and into a stack of threestacked display (e.g., LCoS) Zero-order Suppression (LZOS) gratings 3516(one per color) (elsewhere herein referred to as redirection gratings,e.g., redirection gratings 3114, 3116, and 3118 of FIG. 31A) attached tothe front face 3512 of the substrate 3511.

A proportion of each color incident on the reflective display devices3515 is reflected into a display zero-order beam 3521, and a proportionof each color which is incident upon each display device (e.g., LCoS) isdiffracted by each display device into a corresponding holographic lightfield 3522, e.g., the holographic light field 3220, 3222, 3224 of FIG.32, which may be seen by a viewer. As discussed elsewhere herein, thedisplay zero-order suppression gratings (or redirection gratings) 3516are angle-selective transmission gratings which substantially diffractlight incident upon them at the display zero-order angle butsubstantially transmit light incident upon them at greater or lesserangles, separating the reflected display zero-order light from thediffracted holographic light field. The rejected display zero-orderlight 3523 may exit the front of the redirection gratings at asubstantial angle as shown in FIG. 36B, or may be reflected back intothe shaped substrate 3511 by TIR or by reflection gratings as describedelsewhere herein.

In some embodiments, the tilt angle of the reflective elements 3508 canbe adjusted to achieve greater uniformity of diffraction from thetransmissive field gratings 3513 (e.g., by causing the transmissivefield gratings 3513 to be illuminated at or close to their replay Braggangles), and/or to achieve greater brightness of diffraction from thetransmissive field gratings 3513 (e.g., by causing the transmissivefield gratings 3513 to be illuminated at or close to their replay Braggangles). Such adjustments can be made substantially independently foreach color by adjusting the tilt angle of a respective one of thereflective elements 3508.

In some embodiments, the adjustments can be made as a one-off adjustmentduring manufacture or assembly. Optionally, the adjustments can be madeby the user or installer in the field. In certain embodiments, theadjustments can be performed automatically, for example as part of afeedback loop utilizing color and/or brightness sensors to detect andoptimize optical properties of the holographic light field, e.g.,brightness, uniformity, color uniformity, or white-point. In some cases,the tilt angles of the reflective elements 3508 orthogonal to the tiltangles shown in FIG. 35B are adjusted to optimize the performance of thedisplay system 3500. These approaches can be combined as appropriate.

In some cases, tilt adjustments of the reflective elements 3508 can beused to correct for changes or errors in alignment of the components ofthe display system caused by factors, e.g., manufacturing and assemblytolerances, shipping, storage, and in-use vibration and shock, thermalexpansion and contraction, aging of the gratings, laser-diodes or otherwavelength-dependent components, and wavelength shifts of thelaser-diodes due to aging, operating temperature, operating duty cycle,and/or part-to-part variations.

In some cases, substantially larger or substantially smaller tiltadjustments of the reflective elements 3508 can be used to maintainalignment even if the angle between the expansion prism 3504 and theshaped substrate 3511 is changed substantially from 90° (as shown inFIG. 35B) for example by tilting or rotating the shaped substrate 3511backwards or forwards to tilt the holographic light field respectivelyupwards or downwards.

To achieve relatively uniform illumination on the reflective display3515, the centers of the beams from the laser diodes can be offset,which can also maintain color uniformity in the holographic light field.Small differences in the path travelled by each color to and from thedisplay devices 3515 (in general, primarily due to chromatic dispersionof the beams), for example at their entry into prism element 3504, canotherwise slightly misalign the concentrations of the three colors. Thiscan also be corrected for by adjusting the diffraction efficiency of thereflective display devices 3515 in a spatially variant manner (e.g., inone or two dimensions). Such adjustment can be made on-the-fly as thediffraction efficiency is a function of computer generated holograms(CGHs), or by utilizing elements before or after the display devices3515 with constant or adjustable spatially varying transmissivities orabsorbances (e.g., in one or two dimensions).

In some cases, input light 3517 (e.g., as illustrated in FIG. 36B) intothe substrate 3511 can be p-polarized at the edge surface of thesubstrate 3511 where the input light 3517 enters the substrate 3511 (orthe cover glass 3510 if used) to reduce Fresnel losses at the surface,or the surface can be tilted or anti-reflection coated to reduce suchFresnel losses. A broad-wavelength-band halfwave retarder affixed to thesurface or subsequent to the surface can convert such p-polarization tos-polarization if s-polarization light is the required or desiredpolarization for the transmissive field grating 3513.

In some cases, a broad-wavelength-band retarder positioned between thetransmissive field grating 3513 and the reflective display devices 3515can be used to further adjust the polarization of illumination lightupon the reflective display device 3515 to provide the required ordesired or optimal polarization state for the reflective display devices3515. Such a retarder can be affixed to the exit face of the fieldgrating 3513, or to the outer surface of the reflective display devices3515, or to both, and can be a halfwave plate to provide p-polarizationor s-polarization or can be a quarterwave plate to provide circularpolarization or can have a retardance of another value, which can alsovary spatially and/or temporally and/or by wavelength, to provideoptimal polarization at every point on the reflective display devices3515 for each color. In so far as such a waveplate provides apolarization state, for the reflected holographic light field from thereflective display devices 3515, which may be not the desired or optimalpolarization state for subsequent polarization-dependent elements, e.g.,redirection gratings 3516. In some cases, one or more further waveplatescan be provided prior to such an element or elements with fixed or withspatially or temporally or chromatically varying retardances to furtheradjust the polarization to satisfy the element or elements.

In some cases, an optical distance between the substrate 3511 and thecoupling reflective elements 3508 can be proportionately large to allowthe three colors of light to be separated further at their reflectionsof the reflective elements 3508 so that each color can be reflected by acorresponding reflective element without having to be transmittedthrough one or two other reflective elements, or even made so large thatthe three colors of light separate enough to be reflected using threemirrors with no transmissions through other reflective elements.

In certain embodiments, the coupling reflective elements 3508 can bepositioned and tilted such that the illumination of each of thereflective elements 3508 comes from a substantially different directionrather than from substantially optically-coaxial laser beams. This mayallow the illuminator 3501S to be split into two or three separateilluminators each providing one or two of the three illumination colors,which can be cheaper and/or more efficient than using optics within theilluminator 3501S to combine the light from three laser diodes into acombined white input light which provide input light 3501.

In some embodiments, the shaped substrate 3511 can be formedmonolithically, e.g., by computer numerical control (CNC) machined froma larger block of material, can be formed by optically bonding orindexing two or more simpler (and hence more manufacturable) shapes, orcan be formed by additive or subtractive manufacturing techniques.

In certain embodiments, the reflective display 3515 (or an array ofreflective display devices 3515) with a greater vertical extent can beilluminated by increasing the height of the input light 3517, which issubject to the input light 3517 actually entering the cover glass 3510(which may be omitted) at the tip of the shaped substrate 3511 thatforms a first lower cutoff for display illumination, and subject to theinput light 3517 missing a corner 3518 of the shaped substrate 3511 thatforms an upper cutoff and a second lower cutoff for displayillumination.

In some embodiments, the illumination of the reflective display 3515 isat an angle of approximately 6°, which can be changed to approximately0° because the transmissive field grating 3513 can also act as azero-order suppression element, similar to the redirection gratings3516. In such embodiments, the field grating 3513 can reflect ratherthan transmit, entrapping specularly-reflected zero-order light from thereflective display 3515 within the shaped substrate 3511, where TIR canguide it up and out of the top of the shaped substrate 3511 or into anabsorber 3524 formed thereupon. Using the field grating 3513 at or near0° in combination with the redirection gratings 10016 can reduceresidual display zero-order to a very high degree, e.g., less than 2%residual display zero-order light or even <1%.

In certain embodiments, when one-dimensional suppression gratings areused, the display zero-order suppression appears as a dark band acrossthe reflective display 3515, not a point, with the zero-order of eachillumination color just visible as a point of that color within thisdark band. If the viewer is more likely to look into the reflectivedisplay 3515 from above the normal to the reflective display 3515, as iscommonly the case for a desk or table display, then the system can beconfigured to arrange the band to be above (but, in angular-space, closeto) the holographic light field, where it is less likely to be noticedor objectionable, rather than below or on either side of the holographiclight field. Similarly, if the viewer is more likely to look into thedisplay from below the normal to the reflective display 3515, then thesystem can be configured to arrange the band to be below the holographiclight field. If most viewers look into the display using two eyesdistributed predominantly horizontally, then the band can be arranged atup or below, instead of left or right, of the holographic light field.

In some embodiments in which the illuminator 3501S derives from lightsources with spectral bandwidths on an order of a few nm or a few tensof nm, diffraction in the expansion gratings 3505 and the field gratings3507 can spectrally disperse the illumination light incident upon thereflective display 3515. The illumination light can then exhibitspectral diversity (from the spectral bandwidths of the laser diodes)and spatial diversity (from the dispersion of light from the laserdiodes by these gratings, and, to a lesser extent, from the source sizeof the laser diodes). These multiple orthogonal degrees of diversity cancause significant reduction in visible laser speckle in the holographiclight field, compared to those provided just by the spectral and spatialdiversity of the laser diodes themselves.

In some embodiments, expansion gratings 3505 can be formed with anoptical power such that the expansion gratings 3505 can fully orpartially collimate the input light 3501 in one or two transversedirections, reducing or eliminating the need for laser-diode collimationin the illuminator 3501S.

The incidence angles of the input light 3517 upon the cover plate 3510may be selected such that two or more such incidence angles aresubstantially equal, and in this case the number of reflective elements3508 may be reduced since a single such reflective element may sufficeto reflect two or more colors. Further, the final reflective element in3508 may be provided as a reflective coating upon a surface of, orwithin the substrate of, the previous reflective element, whichsubstrate may be wedged to provide a different reflection angle for thisfinal reflector.

Implementations of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Implementations of the subject matter described inthis specification can be implemented as one or more computer programs,such as, one or more modules of computer program instructions encoded ona tangible, non-transitory computer-storage medium for execution by, orto control the operation of, data processing apparatus. Alternatively orin addition, the program instructions can be encoded on an artificiallygenerated propagated signal, such as, a machine-generated electrical,optical, or electromagnetic signal that is generated to encodeinformation for transmission to suitable receiver apparatus forexecution by a data processing apparatus. The computer-storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them.

The terms “data processing apparatus,” “computer,” or “electroniccomputer device” (or equivalent as understood by one of ordinary skillin the art) refer to data processing hardware and encompass all kinds ofapparatus, devices, and machines for processing data, including by wayof example, a programmable processor, a computer, or multiple processorsor computers. The apparatus can also be or further include specialpurpose logic circuitry, for example, a central processing unit (CPU),an FPGA (field programmable gate array), or an ASIC(application-specific integrated circuit). In some implementations, thedata processing apparatus and special purpose logic circuitry may behardware-based and software-based. The apparatus can optionally includecode that creates an execution environment for computer programs, forexample, code that constitutes processor firmware, a protocol stack, adatabase management system, an operating system, or a combination of oneor more of them. The present specification contemplates the use of dataprocessing apparatuses with or without conventional operating systems.

A computer program, which may also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code, can be written in any form of programming language,including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A computer program may, butneed not, correspond to a file in a file system. A program can be storedin a portion of a file that holds other programs or data, for example,one or more scripts stored in a markup language document, in a singlefile dedicated to the program in question, or in multiple coordinatedfiles, for example, files that store one or more modules, sub-programs,or portions of code. A computer program can be deployed to be executedon one computer or on multiple computers that are located at one site ordistributed across multiple sites and interconnected by a communicationnetwork. While portions of the programs illustrated in the variousfigures are shown as individual modules that implement the variousfeatures and functionality through various objects, methods, or otherprocesses, the programs may instead include a number of sub-modules,third-party services, components, libraries, and such, as appropriate.Conversely, the features and functionality of various components can becombined into single components as appropriate.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, such as, a CPU, a GPU, an FPGA, or an ASIC.

Computers suitable for the execution of a computer program can be basedon general or special purpose microprocessors, both, or any other kindof CPU. Generally, a CPU will receive instructions and data from aread-only memory (ROM) or a random access memory (RAM) or both. The mainelements of a computer are a CPU for performing or executinginstructions and one or more memory devices for storing instructions anddata. Generally, a computer will also include, or be operatively coupledto, receive data from or transfer data to, or both, one or more massstorage devices for storing data, for example, magnetic, magneto-opticaldisks, or optical disks. However, a computer need not have such devices.Moreover, a computer can be embedded in another device, for example, amobile telephone, a personal digital assistant (PDA), a mobile audio orvideo player, a game console, a global positioning system (GPS)receiver, or a portable storage device, for example, a universal serialbus (USB) flash drive, to name just a few.

Computer readable media (transitory or non-transitory, as appropriate)suitable for storing computer program instructions and data include allforms of non-volatile memory, media and memory devices, including by wayof example semiconductor memory devices, for example, erasableprogrammable read-only memory (EPROM), electrically erasableprogrammable read-only memory (EEPROM), and flash memory devices;magnetic disks, for example, internal hard disks or removable disks;magneto-optical disks; and CD-ROM, DVD-R, DVD-RAM, and DVD-ROM disks.The memory may store various objects or data, including caches,look-up-tables, classes, frameworks, applications, backup data, jobs,web pages, web page templates, database tables, repositories storingbusiness and dynamic information, and any other appropriate informationincluding any parameters, variables, algorithms, instructions, rules,constraints, or references thereto. Additionally, the memory may includeany other appropriate data, such as logs, policies, security or accessdata, reporting files, as well as others. The processor and the memorycan be supplemented by, or incorporated in, special purpose logiccircuitry.

To provide for interaction with a user, implementations of the subjectmatter described in this specification can be implemented on a computerhaving a display device, for example, a cathode ray tube (CRT), liquidcrystal display (LCD), light emitting diode (LED), holographic or lightfield display, or plasma monitor, for displaying information to the userand a keyboard and a pointing device, for example, a mouse, trackball,or trackpad by which the user can provide input to the computer. Inputmay also be provided to the computer using a touchscreen, such as atablet computer surface with pressure sensitivity, a multi-touch screenusing capacitive or electric sensing, or other type of touchscreen.Other kinds of devices can be used to provide for interaction with auser as well; for example, feedback provided to the user can be any formof sensory feedback, for example, visual feedback, auditory feedback, ortactile feedback; and input from the user can be received in any form,including acoustic, speech, or tactile input. In addition, a computercan interact with a user by sending documents to and receiving documentsfrom a device that is used by the user; for example, by sending webpages to a web browser on a user's client device in response to requestsreceived from the web browser.

The term “graphical user interface,” or “GUI,” may be used in thesingular or the plural to describe one or more graphical user interfacesand each of the displays of a particular graphical user interface.Therefore, a GUI may represent any graphical user interface, includingbut not limited to, a web browser, a touch screen, or a command lineinterface (CLI) that processes information and efficiently presents theinformation results to the user. In general, a GUI may include multipleuser interface (UI) elements, some or all associated with a web browser,such as interactive fields, pull-down lists, and buttons operable by thebusiness suite user. These and other UI elements may be related to orrepresent the functions of the web browser.

Implementations of the subject matter described in this specificationcan be implemented in a computing system that includes a back-endcomponent, for example, as a data server, or that includes a middlewarecomponent, for example, an application server, or that includes afront-end component, for example, a client computer having a graphicaluser interface or a web browser through which a user can interact withan implementation of the subject matter described in this specification,or any combination of one or more such back-end, middleware, orfront-end components. The components of the system can be interconnectedby any form or medium of wireline or wireless digital datacommunication, for example, a communication network. Examples ofcommunication networks include a local area network (LAN), a radioaccess network (RAN), a metropolitan area network (MAN), a wide areanetwork (WAN), worldwide interoperability for microwave access (WIMAX),a wireless local area network (WLAN) using, for example, 902.11 a/b/g/nand 902.20, all or a portion of the Internet, and any othercommunication system or systems at one or more locations. The networkmay communicate with, for example, internet protocol (IP) packets, framerelay frames, asynchronous transfer mode (ATM) cells, voice, video,data, or other suitable information between network addresses.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

In some implementations, any or all of the components of the computingsystem, both hardware and software, may interface with each other or theinterface using an application programming interface (API) or a servicelayer. The API may include specifications for routines, data structures,and object classes. The API may be either computer language-independentor -dependent and refer to a complete interface, a single function, oreven a set of APIs. The service layer provides software services to thecomputing system. The functionality of the various components of thecomputing system may be accessible for all service consumers via thisservice layer. Software services provide reusable, defined businessfunctionalities through a defined interface. For example, the interfacemay be software written in any suitable language providing data in anysuitable format. The API and service layer may be an integral or astand-alone component in relation to other components of the computingsystem. Moreover, any or all parts of the service layer may beimplemented as child or sub-modules of another software module,enterprise application, or hardware module without departing from thescope of this specification.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or on the scope of what may be claimed, but rather asdescriptions of features that may be specific to particularimplementations of particular inventions. Certain features that aredescribed in this specification in the context of separateimplementations can also be implemented in combination in a singleimplementation. Conversely, various features that are described in thecontext of a single implementation can also be implemented in multipleimplementations separately or in any suitable sub-combination. Moreover,although features may be described as acting in certain combinations andeven initially claimed as such, one or more features from a claimedcombination can in some cases be excised from the combination, and theclaimed combination may be directed to a sub-combination or variation ofa sub-combination.

Particular implementations of the subject matter have been described.Other implementations, alterations, and permutations of the describedimplementations are within the scope of the following claims as will beapparent to those skilled in the art. While operations are depicted inthe drawings or claims in a particular order, this should not beunderstood as requiring that such operations be performed in theparticular order shown or in sequential order, or that all illustratedoperations be performed (some operations may be considered optional), toachieve desirable results. In certain circumstances, multitasking orparallel processing may be advantageous and performed as deemedappropriate.

For the sake of brevity, conventional techniques for construction, use,and/or the like of holographic gratings, LCOS devices, and other opticalstructures and systems may not be described in detail herein.Furthermore, the connecting lines shown in various figures containedherein are intended to represent exemplary functional relationships,signal or optical paths, and/or physical couplings between variouselements. It should be noted that many alternative or additionalfunctional relationships, signal or optical paths, or physicalconnections may be present in an exemplary holographic grating, LCOS, orother optical structure or system, and/or component thereof.

The detailed description of various exemplary embodiments herein makesreference to the accompanying drawings and pictures, which show variousexemplary embodiments by way of illustration. While these variousexemplary embodiments are described in sufficient detail to enable thoseskilled in the art to practice the disclosure, it should be understoodthat other exemplary embodiments may be realized and that logical,optical, and mechanical changes may be made without departing from thespirit and scope of the disclosure. Thus, the detailed descriptionherein is presented for purposes of illustration only and not oflimitation. For example, the steps recited in any of the method orprocess descriptions may be executed in any suitable order and are notlimited to the order presented unless explicitly so stated. Moreover,any of the functions or steps may be outsourced to or performed by oneor more third parties. Modifications, additions, or omissions may bemade to the systems, apparatuses, and methods described herein withoutdeparting from the scope of the disclosure. For example, the componentsof the systems and apparatuses may be integrated or separated. Moreover,the operations of the systems and apparatuses disclosed herein may beperformed by more, fewer, or other components and the methods describedmay include more, fewer, or other steps.

As used in this document, “each” refers to each member of a set or eachmember of a subset of a set. Furthermore, any reference to singularincludes plural exemplary embodiments, and any reference to more thanone component may include a singular exemplary embodiment. Althoughspecific advantages have been enumerated herein, various exemplaryembodiments may include some, none, or all of the enumerated advantages.

Benefits, other advantages, and solutions to problems have beendescribed herein with regard to specific exemplary embodiments. However,the benefits, advantages, solutions to problems, and any elements thatmay cause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as critical, required, or essentialfeatures or elements of the disclosure. The scope of the disclosure isaccordingly limited by nothing other than the appended claims, in whichreference to an element in the singular is not intended to mean “one andonly one” unless explicitly so stated, but rather “one or more.”Moreover, where a phrase similar to ‘at least one of A, B, and C’ or ‘atleast one of A, B, or C’ is used in the claims or specification, it isintended that the phrase be interpreted to mean that A alone may bepresent in an exemplary embodiment, B alone may be present in anexemplary embodiment, C alone may be present in an exemplary embodiment,or that any combination of the elements A, B and C may be present in asingle exemplary embodiment; for example, A and B, A and C, B and C, orA and B and C.

Accordingly, the earlier provided description of example implementationsdoes not define or constrain this specification. Other changes,substitutions, and alterations are also possible without departing fromthe spirit and scope of this specification.

1.-271. (canceled)
 272. An optical device comprising: a first optically diffractive component comprising a first diffractive structure configured to diffract a first color of light having a first incident angle at a first diffracted angle; a second optically diffractive component comprising a second diffractive structure configured to diffract a second color of light having a second incident angle at a second diffracted angle; a first reflective layer configured to totally reflect the first color of light having the first incident angle and transmit the second color of light having the second incident angle; and a second reflective layer configured to totally reflect the second color of light having the second incident angle, wherein the first reflective layer is between the first and second diffractive structures, and the second diffractive structure is between the first and second reflective layers.
 273. The optical device of claim 272, further comprising: a color-selective polarizer between the first and second diffractive structures, wherein the first diffractive structure is configured to: i) diffract the first color of light in a first polarization state incident at the first incident angle with a first diffraction efficiency; and ii) diffract the second color of light in a second polarization state incident at the second incident angle with a diffraction efficiency that is substantially smaller than the first diffraction efficiency, wherein the color-selective polarizer is configured to rotate a polarization state of the second color of light in the second polarization state incident on the color-selective polarizer from the second polarization state to the first polarization state, and wherein the second diffractive structure is configured to diffract the second color of light in the first polarization state incident at the second incident angle with a second diffraction efficiency.
 274. The optical device of claim 272, further comprising: a side surface; and an optical absorber attached to the side surface and configured to absorb totally reflected light of the first and second colors.
 275. The optical device of claim 272, wherein the first reflective layer is configured to have a refractive index smaller than that of a layer of the first optically diffractive component that is immediately adjacent to the first reflective layer, such that the first color of light having the first incident angle is totally reflected by an interface between the first reflective layer and the layer of the first optically diffractive component, without totally reflecting the second color of light having the second incident angle.
 276. The optical device of claim 272, wherein the first optically diffractive component comprises a first carrier film and a first diffraction substrate attached to opposite sides of the first diffractive structure, the first carrier film being closer to the second diffractive structure than the first diffraction substrate, and wherein the first carrier film comprises the first reflective layer.
 277. The optical device of claim 272, wherein the second optically diffractive component comprises a second carrier film and a second diffraction substrate attached to opposite sides of the second diffractive structure, the second diffraction substrate being closer to the first diffractive structure than the second carrier film, and wherein the second reflective layer is attached to the second carrier film.
 278. The optical device of claim 272, further comprising: a third optically diffractive component comprising a third diffractive structure configured to diffract first and zero orders of a third color of light incident at a third incident angle on the third diffractive structure, the first order being diffracted at a third diffracted angle, and the zero order being transmitted at the third incident angle, wherein the second reflective layer is between the second diffractive structure and the third diffractive structure, and wherein each of the first and second reflective layers is configured to transmit the third color of light incident at the third incident angle.
 279. The optical device of claim 278, further comprising: a third reflective layer configured to totally reflect the third color of light incident at the third incident angle on the third reflective layer, wherein the third diffractive structure is between the second and third reflective layers.
 280. The optical device of claim 278, wherein the second optically diffractive components comprises a second diffraction substrate and a second carrier film arranged on opposite sides of the second diffractive structure, wherein the third optically diffractive component comprises a third carrier film and a third diffraction substrate positioned on opposite sides of the third diffractive structure, and wherein the second reflective layer is between the second and third carrier films.
 281. The optical device of claim 272, wherein each of the first and second diffractive structure comprises a respective holographic grating formed in a recording medium, wherein each of the first and second optically diffractive components comprises a respective Bragg grating formed in the recording medium, wherein the respective Bragg grating comprises a plurality of fringe planes with a fringe tilt angle θ_(t) and a fringe spacing Λ perpendicular to the fringe planes in a volume of the recording medium, and wherein the respective Bragg grating is configured such that, when an incident angle on the recording medium is an on-Bragg angle, a respective diffracted angle θ_(m) is satisfied with Bragg's equation as below: mλ=2nΛ sin(θ_(m)−θ_(t)), where k represents a respective wavelength of a color of light in vacuum, n represents a refractive index in the recording medium, θ_(m) represents m^(th) diffraction order Bragg angle in the recording medium, θ_(t) represents the fringe tilt in the recording medium, and wherein each of the first and second incident angles is substantially identical to a respective on-Bragg angle, and each of the first and second diffracted angles is substantially identical to a respective first order Bragg angle.
 282. The optical device of claim 281, wherein a thickness of the recording medium is more than one order of magnitude larger than the fringe spacing.
 283. The optical device of claim 272, wherein the first diffracted angle and the second diffracted angle are substantially identical to each other, and wherein each of the first and second diffracted angles is in a range from −10 degree to 10 degree.
 284. The optical device of claim 272, wherein the first color of light has a wavelength smaller than the second color of light, wherein the first incident angle of the first color of light is larger than the second incident angle of the second color of light, and wherein each of the first and second incident angles is in a range from 70 degree to 90 degree.
 285. The optical device of claim 272, comprising a plurality of components including the first optically diffractive component and the second optically diffractive component, wherein adjacent two components of the plurality of components are attached together by an intermediate layer that comprises at least one of a refractive index matching material, an OCA, a UV-cured or heat-cured optical glue, or an optical contacting material.
 286. The optical device of claim 285, wherein the second reflective layer comprises a corresponding intermediate layer.
 287. The optical device of claim 272, further comprising a substrate having a back surface attached to a front surface of the first optically diffractive component.
 288. The optical device of claim 287, wherein the substrate comprises a side surface angled to the back surface and is configured to receive a plurality of different colors of light at the side surface, wherein an angle between the side surface and the back surface of the substrate is no less than 90 degree, and wherein the substrate is configured such that the plurality of different colors of light are incident on the side surface with an incident angle substantially identical to 0 degree.
 289. The optical device of claim 287, wherein the substrate is wedged and comprises a titled front surface, and wherein an angle between the front surface and the side surface is less than 90 degree.
 290. An optical device, comprising: at least two optically diffractive components; and at least one reflective layer, wherein the optical device is configured such that, when light of different colors is incident on the optical device, the optical device separates light of individual colors of the different colors while suppressing crosstalk between the different colors, and wherein the at least one reflective layer is configured for total internal reflection of light of at least one of the different colors.
 291. The optical device of claim 290, wherein the optical device is configured such that an output light beam diffracted by the optical device comprises only light of a particular color of the different colors without crosstalk from one or more other colors of the different colors.
 292. The optical device of claim 290, wherein the at least one reflective layer is configured to totally reflect zero order light of a particular color of the different colors transmitted by a respective one of the optically diffractive component, while transmitting one or more other colors of the different colors
 293. The optical device of claim 290, wherein the optical device is configured such that, when the light of different colors is incident on the optical device, each of the optically diffractive components diffracts light of a respective color of the different colors.
 294. The optical device of claim 290, wherein the optically diffractive components comprise at least one of one or more transmissive diffractive structures or one or more reflective diffractive structures, and wherein each of the at least one of the one or more transmissive diffractive structures or the one or more reflective diffractive structures is configured to light of a respective color of the different colors.
 295. The optical device of claim 290, further comprising: at least one color-selective polarizer configured to rotate a polarization state of light of at least one color of the different colors, such that light of a particular color of the different colors is incident in a first polarization state on a respective one of the optically diffractive components, while light of one or more other colors of the different colors is incident in a second polarization state different from the first polarization state on the respective one of the optically diffractive components.
 296. An optical device comprising: a first optically diffractive component comprising a first diffractive structure configured to: i) diffract first and zero orders of a first color of light incident at a first incident angle on the first diffractive structure, the first order being diffracted at a first diffracted angle, and the zero order being transmitted at the first incident angle; and ii) transmit a second color of light incident at a second incident angle on the first diffractive structure; a first reflective layer configured to: i) totally reflect the first color of light incident on the first reflective layer at the first incident angle; and ii) transmit the second color of light incident on the first reflective layer at the second incident angle; a second optically diffractive component comprising a second diffractive structure configured to diffract first and zero orders of the second color of light incident at the second incident angle on the second diffractive structure, the first order being diffracted at a second diffracted angle, and the zero order being transmitted at the second incident angle; and a second reflective layer configured to totally reflect the second color of light incident on the second reflective layer at the second incident angle, wherein the first reflective layer is between the first and second diffractive structures, and the second diffractive structure is between the first and second reflective layers.
 297. A method comprising: transmitting at least one timing control signal to an illuminator to activate the illuminator to emit a plurality of different colors of light onto an optical device, such that the optical device converts the plurality of different colors of light to individually diffracted colors of light to illuminate a display comprising a plurality of display elements; and transmitting, for each of the plurality of display elements of the display, at least one respective control signal to modulate the display element, such that the individually diffracted colors of light are reflected by the modulated display elements to form a multi-color three-dimensional light field corresponding to the respective control signals, wherein the optical device comprises: a first optically diffractive component comprising a first diffractive structure; a second optically diffractive component comprising a second diffractive structure; a first reflective layer; and a second reflective layer, wherein: the first reflective layer is between the first and second diffractive structures; the second diffractive structure is between the first and second reflective layers; when a first color of light is incident at a first incident angle on the first diffractive structure, the first diffraction structure diffracts first and zero orders of the first color, the first order being diffracted at a first diffracted angle, and the zero order being transmitted at the first incident angle; when a second color of light is incident at a second incident angle on the first diffractive structure, the first diffraction grating transmits the second color of light at the second incident angle; when the first color of light is incident on the first reflective layer at the first incident angle, the first reflective layer totally reflects the first color of light; when the second color of light is incident on the first reflective layer at the second incident angle, the reflective layer transmits the second color of light at the second incident angle; when the second color of light is incident at the second incident angle on the second diffractive structure, the second diffractive structure diffracts first and zero orders of the second color of light, the first order being diffracted at a second diffracted angle, and the zero order being transmitted at the second incident angle; and when the second color of light is incident on the second reflective layer at the second incident angle, the second reflective layer totally reflects the second color of light.
 298. The optical device of claim 297, further comprising: obtaining graphic data comprising respective primitive data for a plurality of primitives corresponding to an object in a three-dimensional space; determining, for each of the plurality of primitives, an electromagnetic (EM) field contribution to each of the plurality of display elements of the display by calculating, in a three-dimensional coordinate system, an EM field propagation from the primitive to the display element; generating, for each of the plurality of display elements, a sum of the EM field contributions from the plurality of primitives to the display element; and generating, for each of the plurality of display elements, the respective control signal based on the sum of the EM field contributions to the display element for modulation of at least one property of the display element, wherein the multi-color three-dimensional light field corresponds to the object.
 299. The optical device of claim 298, comprising: sequentially modulating the display with information associated with the plurality of different colors in a series of time periods, and controlling the illuminator to sequentially emit each of the plurality of different colors of light to the optical device during a respective time period of the series of time periods, such that each of the plurality of different colors of light is diffracted by the optical device to the display and reflected by the modulated display elements of the display to form a respective color three-dimensional light field corresponding to the object during the respective time period.
 300. The optical device of claim 297, wherein the plurality of different colors of light are diffracted by the optical device at a substantially same diffracted angle to the display, and wherein the diffracted angle is within a range from −10 degree to 10 degree.
 301. The optical device of claim 297, wherein the illuminator and the optical device are configured such that the plurality of different colors of light are incident on the first optically diffractive component of the optical device with respective incident angles, and wherein each of the respective incident angles is in a range from 70 degree to 90 degree. 